Right Triangle

Problem 201

If the adjacent side of a triangle is 56.7 units long, and the hypotenuse is 71.2 units long, what is the length of the side opposite? (A) 41.23 units (B) 43.02 units (C) 43.06 units (D) 42.27 units

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Problem 202

If the opposite side of a triangle is 12.4 units long, and the hypotenuse is 67.8 units long, what is the length of the side adjacent? (A) 66.54 units (B) 66.65 units (C) 66.66 units (D) 66.67 units

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Problem 203

Evaluate $\cos \frac{\pi}{4}$ using special right triangles and simplify your answer.

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Problem 204

Evaluate $\cot \frac{\pi}{3}$ using special right triangles. Simplify your answer with integers or fractions.

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Problem 205

Find the six trigonometric functions for angle $\theta$ in a right triangle where the opposite side is 16 and adjacent side is 12.

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Problem 206

Dalam segitiga $PQR$ dengan $\tan \theta=\frac{5}{12}$ , cari nilai $\sin \alpha$ terkait $\alpha$ dan $\theta$ .

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Problem 207

Evaluate the expression using special right triangles:
$\frac{\sec ^{2} \frac{\pi}{3}+\tan ^{2} \frac{\pi}{4}}{\cot ^{2} \frac{\pi}{6}}=$
Simplify your answer, including radicals.

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Problem 208

If $\sec \theta=6$ , find $\csc \theta$ , $\cot \theta$ , $\sin \theta$ , $\cos \theta$ , and $\tan \theta$ .

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Problem 209

Find the sine of $\angle T$ .
Write your answer in simplified, rationalized form. Do not round. $\sin (T)=$ $\square$

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Problem 210

Solve for $x$ in the triangle. Round your answer to the nearest tenth. $x=$

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Problem 211

A night triangle has side lengths 5,12 , and 13 as shown below. Use these lengths to find $\cos B, \tan B$ , and $\sin B$ . $\begin{array}{l} \cos B= \\ \tan B= \\ \sin B= \end{array}$ $\square$ $\square$ $\square$

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Problem 212

A right triangle has side lengths 5,12 , and 13 as shown below. Use these lengths to find $\tan M, \sin M$ , and $\cos M$ . $\begin{array}{l} \tan M=\square \\ \sin M=\square \\ \cos M=\square \end{array}$

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Problem 213

Select the correct answer.
In $\triangle A B C, \angle A$ is a right angle. What is the value of $y$ ? A. $7 \sin \frac{\pi}{6}$ B. $7 \cos \frac{\pi}{6}$ C. $7 \tan \frac{\pi}{6}$ D. 7

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Problem 214

Select the correct answer.
Given a right triangle, if $\tan \theta=\frac{(3)}{(4)}$ , what is the length of the side adjacent to $\angle \theta ?$ A. 3 B. 4 C. 5 D. 75

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Problem 215

Select the correct answer.
In a right triangle, if $\angle \theta=39^{\circ}$ and the side adjacent to $\angle \theta$ is equal to 12.0 centimeters, what is the approximate length of the opposite side? A. 7.6 centimeters B. 9.3 centimeters C. 9.7 centimeters D. 14.8 centimeters

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Problem 216

Type the correct answer in the box. Round your answer to the nearest integer.
A train traveled a distance of 1 mile, or 5,280 feet, while climbing a hill at an angle of $5^{\circ}$ .
The vertical height that the train climbed is approximately $\square$ feet.

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Problem 217

For the triangle shown below, use your calculator to solve for the missing sides and angles. $\theta=$ $\square$ degrees $f=$ $\square$ $e=$ $\square$ Round your answers to two decimal places. Question Help: Video 1 Video 2

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Problem 218

3. Find the sine of angle A. Give your answer as a fraction in simplest form. $\operatorname{Sin} A=$ $\qquad$ I - Choose the correct answer - $\qquad$
Clear All

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Problem 219

Solve the right triangle shown in the figure for all unknown sides and angles. Round your answers to two decimal places $\begin{aligned} & B=78.7^{\circ}, \quad a=4.9 \\ A & =\square^{\circ} \\ c & =\square^{\circ} \\ b & =\square^{\circ} \\ c & =\square^{\circ} \end{aligned}$

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Problem 220

A 165 -foot tall antenna has 4 guy-wires connected to the top of the antenna, and each guy-wire is anchored to the ground. A side-view of this scenario is shown.
One of the guy-wires forms an angle of $\alpha=0.3$ radians with the antenna and the opposing guy-wire forms an angle of $\beta=0.41$ radians with the antenna. a. What is the horizontal distance between anchor 1 and the base of the antenna? $165^{} \tan (0.3)$ $\qquad$ $\star$ feet $\square$ $165 \cdot \tan (0.3)=51.040481185587836$ . b. What is the horizontal distance between anchor 2 and the base of the antenna? $165^{} \tan (0.41)$ $\square$ $\otimes$ feet $\square$ $165 \cdot \tan (0.41)=71.71414875898176$ . c. What is the distance between anchor 1 and anchor 2? $\square$ feet Preview

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Problem 221

7. Nate is in a meadow standing exactly 185 ft from the base of a mountain. He sees someone climbing the mountain in his binoculars. His eyes are 6 ft above the ground, and is angle of elevation is $10^{\circ}$ . How far above the ground is the climber?

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Problem 222

8. An airplane must fly over a 120 ft tower. The plane is 400 ft away from the tower when it begins to climb. At what angle should the plane climb to make it over the tower?

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Problem 223

Gina and Hone are on opposite sides of a tower. Gina is 20 m away with an angle of elevation of $53^{\circ}$ . Hone's angle is $37^{\circ}$ . Find Hone's distance from the tower.

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Problem 224

Peter sees a flag-pole $6 \mathrm{~m}$ away. Angle of depression is $65^{\circ}$ , and elevation is $47^{\circ}$ . Find the height.

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Problem 225

14. [0/1 Points]
DETAILS MY NOTES SPRECALC8 6.2.067. PREVIOUS ANSWERS ASK YOUR TEACHER PRACTICE ANOTHER elevation is found to be $36^{\circ}$ . Estimate the height of the mountain (in ft ). (Round your answer to the nearest foot.) 4477 $x \mathrm{ft}$
Need Help? Read It Watch it

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Problem 226

Find $\sin \theta$ , where $\theta$ is the angle shown. Give an exact value, not a decimal approximation. $\sin \theta=$ $\square$

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Problem 227

(2.) Using the appropriate special triangle, determine $\theta$ if $0^{\circ} \leq \theta \leq 90^{\circ}$ . a) $\sin \theta=\frac{\sqrt{3}}{2}$ c) $2 \sqrt{2} \cos \theta=2$ b) $\sqrt{3} \tan \theta=1$ d) $2 \cos \theta=\sqrt{3}$

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Problem 228

A calculator is allowed for this question. A person is standing 50 ft from a statue. The person looks up at an angle of elevation of $16^{\circ}$ when staring at the top of the statue. Then the person looks down at an angle of depression of $8^{\circ}$ when staring at the base of the statue. How tall is the statue to the nearest tenth of a foot?

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Problem 229

4. From the top of the tower 30 m height a man is observing the base of a tree at an angle of depression measuring $30^{\circ}$ . Find the distance between the tree and the tower.

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Problem 230

6. A ladder is leaning against a vertical wall makes an angle of $50^{\circ}$ with the ground. The foot of the ladder is 3 ft from the wall. Find the length of ladder.

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Problem 231

Find the exact value of $\tan \frac{\theta}{2}$ for the angle $\theta$ shown in the right triangle:
Given: $\tan \frac{\theta}{2}= \pm \sqrt{\frac{1-\cos \theta}{1+\cos \theta}}$ $\tan \frac{\theta}{2}=\frac{\sin \theta}{1+\cos \theta}$ $\tan \frac{\theta}{2}=\frac{1-\cos \theta}{\sin \theta}$

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Problem 232

Find the angle of bend $a$ in a right triangle where the rise is 14" and the base is 34". Choices: $22.38 \mathrm{deg}$ , $21.25 \mathrm{deg}$ , $42.97 \mathrm{deg}$ , $37.65 \mathrm{deg}$ .

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Problem 233

Find the hypotenuse of a right triangle with a $32^{\circ}$ angle and an opposite side of 12. Round to the nearest hundredth.

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Problem 234

Question Watch Video Show Examples
The angle of elevation to a nearby tree from a point on the ground is measured to be $20^{\circ}$ . How tall is the tree if the point on the ground is 92 feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary. Answer Attempt 2 out of 2

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Problem 235

If a tree has a height of 165 feet, what would be the angle of elevation from level ground measured from 95 feet away? Round your answer to the nearest tenth of a degree.

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Problem 236

6. Consider the triangle in the following figure, where the lengths of the three sides are $a, b, c$ , and the angles are $\angle A, \angle B$ , and $\angle C$ . Note $\angle C$ is a right angle.
Assume $\angle A=40^{\circ}$ and $a=5$ . (a) (1 point) Write down the value of $\angle B$ in radians. (b) (1 point) Use an appropriate trig function to express the value of $b$ . (c) (1 point) Use an appropriate trig function to express the value of $c$ .

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Problem 237

Use $\triangle D E F$ to calculate exact values of sine, cosine, and tangent for $30^{\circ}$ and $60^{\circ}$ .

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Problem 238

Find the exact value of $\cos{G}$ in simplest radical form.
$\cos{G} =$
Answer Attempt 1 out of 2 Submit Answer

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Problem 239

3. 5. 6. 4.

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Problem 240

Find the length of an escalator at a $35^{\circ}$ angle that covers a vertical distance of 16 feet. Round to 1 decimal place.

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Problem 241

Find the angle $\theta$ made by a 67-foot rope anchored 37.2 feet from a vertical pole using $\tan(\theta) = \frac{37.2}{67}$ .

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Problem 242

Find the height of a hill with a road at a $5.4^{\circ}$ angle and a length of 3.1 miles. Round to 2 decimal places.

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Problem 243

Find the distance from a rock to a tree, given a stake 24.0 yards north of the rock with a bearing of $S 16.0^{\circ} W$ . Round to the nearest tenth of a yard.

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Problem 244

A boat sails N 38° 10' W for 78.3 miles. Find the north and west distances traveled, rounded to the nearest tenth.

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Problem 245

Solve the right triangle $A B C$ for all missing parts. Express angles in decimal degrees. $\mathrm{A}=22^{\circ} 16^{\prime}, \mathrm{c}=21.75 \mathrm{~m}$ $B \approx$ $\square$ - (Round to the nearest hundredth as needed.)

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Problem 246

Find the length of the rafter shown.
The length of the rafter is $\square$ in. (Round to the nearest inch as needed.)

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Problem 247

Find the value of $\sin W$ rounded to the nearest hundredth, if necessary.

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Problem 248

Solve for $x$ . Round to the nearest tenth, if necessary. $52$ $18^\circ$ $x$ D E F

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Problem 249

Find $\cos \theta$ if $\tan \theta=\frac{4}{3}$ . Options: $\frac{3}{5}$ , $\frac{3}{4}$ , $\frac{5}{3}$ , $\frac{4}{5}$ .

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Problem 250

Solve the right triangle.
$Q$ $6.1$ $P$ $41^\circ$ $R$
Write your answers as integers or as decimals rounded to the nearest tenth. $QR =$ $PR =$ $m\angle Q =$

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Problem 251

A tower is located 239.1 ft from a building. From a window in the building, a person measures an angle of elevation of $42^{\circ}$ to the top of the building, and an angle of depression of $16.8^{\circ}$ to the base of the tower. Find the height of the tower. $\qquad$ ft

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Problem 252

Use the image to answer the question.
2 ft.
Ramp up to the house
$20^\circ$
Tyrese is building a ramp up to his home. He knows the height of the ramp is 2 feet. If the angle of elevation of the ramp is $20^\circ$ , how long does the ramp have to be?
(1 point)

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Problem 253

Find the exact value of $\tan J$ in simplest radical form.
Answer Attempt 1 out of 2 $\tan J=$ $\square$ Submit Answer $\square$

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Problem 254

Question Watch Video Show Examples
Find the exact value of $\sin M$ in simplest radical form.
Answer Attempt 1 out of 2 $\sin M=$ $\square$ Submit Answer

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Problem 255

+ R 90 60' Which equation gives the correct value for RQ? tan 60=90/RQ sin 60-90/RQ cos 60=90/RQ tan 60=90/x Michael Belton Type here to search - Top 10 SNL Impressio... 人口ˇ 8:49 AM 12/9/2024

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Problem 256

Use the information contained in the figure to determine the values of the six trigonometric functions of $\theta$ . Write the exact answers and simplify. Do not round.
Answer 4 Points
$\sin\theta =$ $\cos\theta =$ $\tan\theta =$ $\csc\theta =$ $\sec\theta =$ $\cot\theta =$ Keypad Keyboard Shortcuts

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Problem 257

$2$ X $10$ Y $5$ $5\sqrt{3}$ Z \sin{X} = \text{______}

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Problem 258

Type decimal answer to the nearest tenth place Find DF to the nearest tenth. $10.0$ $43.6^\circ$

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Problem 259

1) Practice $3$ $5$ $4$ B C $\sin(\angle A) =$ 2) $8$ $17$ C A $\sin(\angle A) =$ 3) A $20$ $29$ $21$ C B $\sin(\angle A) =$ 4) P $8$ $10$ N $6$ M $\sin(\angle P) =$

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Problem 260

Basic Trig: Cosine 8) 5 9) 29 4 21 $\cos(\angle A) =$ $\cos(\angle A) =$ 10) 17 8 $\cos(\angle B) =$ Basic Trig: Tangent Practice 11) 5 12) 17 3 8 4 $\tan(\angle A) =$ $\tan(\angle A) =$

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Problem 261

Find the tangent of $\angle B$ .
$10$ $\sqrt{14}$
Write your answer in simplified, rationalized form. Do not round.
$\tan(B) =$

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Problem 262

26° 15

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Problem 263

$x =$ $9$ $65^\circ$ $x$

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Problem 264

Solve for $x$ in the triangle. Round your answer to the nearest tenth. $55^{\circ}$ $12$ $x$

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Problem 265

A kite flying in the air has an 86-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is $53^\circ$ . Find the height of the kite. Round your answer to the nearest tenth. 86 $53^\circ$ ft

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Problem 266

Find x. Round your answer to the nearest tenth of a degree. $x = \Box^{\circ}$ 13 9

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Problem 267

A person is standing 150 feet from the base of a statue. If the statue is sitting on the ground and is 21 feet tall, what is the angle of elevation from the person's eye to the top of the statue? Assume the person's eye-level is 5.5 feet above the ground. 5.9° 7.3° 6.2° 8.0°

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Problem 268

(1) $a=$

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Problem 269

Find $\tan A$ in triangle $ABC$ (right angle at $C$ ) with sides $a=6$ and $b=7$ . Provide exact answers.

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Problem 270

Find $\sin A$ for right triangle $\mathrm{ABC}$ with sides $a=5$ and $b=3$ . Exact answers only.

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Problem 271

Find $\cos A$ for a right triangle with sides $a=5$ and $b=2$ . Provide the exact answer with a rational denominator.

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Problem 272

Find the value of $\cot A$ in triangle $ABC$ where $b=5$ and $c=6$ . Provide exact answers with rational denominators.

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Problem 273

Find the length of a guy wire attached 10 ft from the top of a 230 ft tower at a $32^{\circ}$ angle. Round to the nearest tenth.

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Problem 274

Find $\csc B$ for a right triangle with sides $a=5$ and $b=6$ . Provide exact answers with rational denominators.

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Problem 275

In a right triangle with hypotenuse 100km and opposite side 60km, find $\sin \theta = \frac{60}{100}$ .

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Problem 276

Find $\sec \theta$ given $\tan \theta = \frac{9}{40}$ and $\theta$ is in QIII. $\sec \theta =$

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Problem 277

Let $\angle D$ be an acute angle. Use a calculator to approximate the measure of $\angle D$ to the nearest tenth of a degree. $\begin{array}{l} \sin D=0.31 \\ m \angle D= \end{array}$ $\square$

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Problem 278

Find the measure of side $c$ .
$a = 33$ m
$31^\circ$
$c = \boxed{\phantom{00}}$ m (Round the answer to the nearest whole number.)

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Problem 279

Solve the right triangle.
Write your answers as integers or as decimals rounded to the nearest tenth. $\begin{aligned} G H & =\square \\ H I & =\square \\ m \angle G & =\square \end{aligned}$ Submit

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Problem 280

190 COMPLETA utilizzando la calcolatrice. Determina $x$ e $y$ e approssima il risultato a una cifra decimale. - 2

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Problem 281

A 7 - ft ladder leans against the side of a house. How far Is the bottom of the ladder from the side of the house when the angle of elevation of the ladder Is $64^{\circ}$ ? Round your answer to the nearest tenth. $\square$ ft Check Save For Later Submit Assian

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Problem 282

4. Solve for $x$ . Round your answer to the nearest tenth. $x=$ Previous

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Problem 283

Note: Triangle may not be drawn to scale. Suppose $\mathrm{a}=9$ and $\mathrm{b}=4$ .
Find an exact value or give at least two decimal places: $\sin (A)=$ $\square$ $\cos (A)=$ $\square$ $\tan (A)=$ $\square$ $\sec (A)=$ $\square$ $\csc (A)=$ $\square$ $\cot (A)=$ $\square$

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Problem 284

Note: Triangle may not be drawn to scale. Suppose $\mathrm{a}=11$ and $\mathrm{A}=25$ degrees. Find: $b=$ $\square$ $c=$ $\square$ $B=$ $\square$ degrees
Give all answers to at least one decimal place. Give angles in degrees

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Problem 285

Find $v$ .
Write your answer in simplest radical form. $\square$ kilometers Submit

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Problem 286

A 52.93 ft tall building casts a 56.57 ft shadow. Find the sun's angle of elevation to the nearest hundredth of a degree.

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Problem 287

Find the distance to the base of a plateau 19.6 m high with an elevation angle of $16.5^{\circ}$ . Round to one decimal place.

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Problem 288

12. From the given data, which trig ratio will you use to solve for side $x$ in the $\Delta$ below? $\qquad$

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Problem 289

Course: Finite Math 4th Period
Use the given right triangle to find ratios, in reduced form, for $\sin \mathrm{A}, \cos \mathrm{A}$ , and $\tan \mathrm{A}$ .
Enter the ratios in reduced form: $\begin{aligned} \sin A & =5 / 13 \\ \cos A & =5 / 12 / 13 \\ \tan A & =5 / 12 \end{aligned}$

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Problem 290

ement of the progress bor moy be uneven because questions can be worth more or less (including zero) depending A 25 -foot-long footbridge has two diagonal supports that meet in the center of the bridge. Each support makes a $65^{\circ}$ angle with a short vertical support.
What is the length $x$ of a diagonal support, to the nearest tenth of a foot? $x \approx$ $\qquad$ feet
The solution is

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Problem 291

Find the missing side. Round to the nearest tenth. 15) 17)

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Problem 292

18)

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Problem 293

What is $\cos 28^{\circ} ?$ A. $\frac{15}{17}$ B. $\frac{8}{17}$ c. $\frac{8}{15}$ D. $\frac{15}{8}$

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Problem 294

Find the sine, cosine, and tangent of $\angle G$ .
Write your answer in simplified, rationalized form. Do not round. $\begin{array}{l} \sin (G)=\square \\ \cos (G)=\square \\ \tan (G)=\square \end{array}$

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Problem 295

Solve for $x$ . Round to the nearest tenth, if necessary.

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Problem 296

c) Find side $x$ .

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Problem 297

Find the angle of elevation of the sun for a 64.38 ft tall building with a 69.19 ft shadow. Round to the nearest hundredth.

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Problem 298

Find the value of $y$ . Round your answer to the nearest tenth.

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Problem 299

Find the missing side length. Round to the nearest tenth.

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Problem 300

$\begin{array}{l} c=17 \\ B=29^{\circ} \end{array}$

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1 2 3 4

Right Triangle

Problem 201

If the adjacent side of a triangle is 56.7 units long, and the hypotenuse is 71.2 units long, what is the length of the side opposite? (A) 41.23 units (B) 43.02 units (C) 43.06 units (D) 42.27 units

Problem 202

If the opposite side of a triangle is 12.4 units long, and the hypotenuse is 67.8 units long, what is the length of the side adjacent? (A) 66.54 units (B) 66.65 units (C) 66.66 units (D) 66.67 units

Problem 203

Evaluate cos⁡π4\cos \frac{\pi}{4}cos4π​ using special right triangles and simplify your answer.

Problem 204

Evaluate cot⁡π3\cot \frac{\pi}{3}cot3π​ using special right triangles. Simplify your answer with integers or fractions.

Problem 205

Find the six trigonometric functions for angle θ\thetaθ in a right triangle where the opposite side is 16 and adjacent side is 12.

Problem 206

Dalam segitiga PQRPQRPQR dengan tan⁡θ=512\tan \theta=\frac{5}{12}tanθ=125​, cari nilai sin⁡α\sin \alphasinα terkait α\alphaα dan θ\thetaθ.

Problem 207

Evaluate the expression using special right triangles: sec⁡2π3+tan⁡2π4cot⁡2π6= \frac{\sec ^{2} \frac{\pi}{3}+\tan ^{2} \frac{\pi}{4}}{\cot ^{2} \frac{\pi}{6}}= cot26π​sec23π​+tan24π​​= Simplify your answer, including radicals.

Problem 208

If sec⁡θ=6\sec \theta=6secθ=6, find csc⁡θ\csc \thetacscθ, cot⁡θ\cot \thetacotθ, sin⁡θ\sin \thetasinθ, cos⁡θ\cos \thetacosθ, and tan⁡θ\tan \thetatanθ.

Problem 209

Find the sine of ∠T\angle T∠T.Write your answer in simplified, rationalized form. Do not round. sin⁡(T)=\sin (T)=sin(T)= □\square□

Problem 210

Solve for xxx in the triangle. Round your answer to the nearest tenth. x=x=x=

Problem 211

A night triangle has side lengths 5,12 , and 13 as shown below. Use these lengths to find cos⁡B,tan⁡B\cos B, \tan BcosB,tanB, and sin⁡B\sin BsinB. cos⁡B=tan⁡B=sin⁡B=\begin{array}{l} \cos B= \\ \tan B= \\ \sin B= \end{array}cosB=tanB=sinB=​ □\square□ □\square□ □\square□

Problem 212

A right triangle has side lengths 5,12 , and 13 as shown below. Use these lengths to find tan⁡M,sin⁡M\tan M, \sin MtanM,sinM, and cos⁡M\cos McosM. tan⁡M=□sin⁡M=□cos⁡M=□\begin{array}{l} \tan M=\square \\ \sin M=\square \\ \cos M=\square \end{array}tanM=□sinM=□cosM=□​

Problem 213

Select the correct answer.In △ABC,∠A\triangle A B C, \angle A△ABC,∠A is a right angle. What is the value of yyy ? A. 7sin⁡π67 \sin \frac{\pi}{6}7sin6π​ B. 7cos⁡π67 \cos \frac{\pi}{6}7cos6π​ C. 7tan⁡π67 \tan \frac{\pi}{6}7tan6π​ D. 7

Problem 214

Select the correct answer.Given a right triangle, if tan⁡θ=(3)(4)\tan \theta=\frac{(3)}{(4)}tanθ=(4)(3)​, what is the length of the side adjacent to ∠θ?\angle \theta ?∠θ? A. 3 B. 4 C. 5 D. 75

Problem 215

Problem 216

Type the correct answer in the box. Round your answer to the nearest integer.A train traveled a distance of 1 mile, or 5,280 feet, while climbing a hill at an angle of 5∘5^{\circ}5∘.The vertical height that the train climbed is approximately □\square□ feet.

Problem 217

For the triangle shown below, use your calculator to solve for the missing sides and angles. θ=\theta=θ= □\square□ degrees f=f=f= □\square□ e=e=e= □\square□ Round your answers to two decimal places. Question Help: Video 1 Video 2

Problem 218

3. Find the sine of angle A. Give your answer as a fraction in simplest form. Sin⁡A=\operatorname{Sin} A=SinA= \qquad I - Choose the correct answer - \qquadClear All

Problem 219

Problem 220

Problem 221

7. Nate is in a meadow standing exactly 185 ft from the base of a mountain. He sees someone climbing the mountain in his binoculars. His eyes are 6 ft above the ground, and is angle of elevation is 10∘10^{\circ}10∘. How far above the ground is the climber?

Problem 222

8. An airplane must fly over a 120 ft tower. The plane is 400 ft away from the tower when it begins to climb. At what angle should the plane climb to make it over the tower?

Problem 223

Gina and Hone are on opposite sides of a tower. Gina is 20 m away with an angle of elevation of 53∘53^{\circ}53∘. Hone's angle is 37∘37^{\circ}37∘. Find Hone's distance from the tower.

Problem 224

Peter sees a flag-pole 6 m6 \mathrm{~m}6 m away. Angle of depression is 65∘65^{\circ}65∘, and elevation is 47∘47^{\circ}47∘. Find the height.

Problem 225

14. [0/1 Points]DETAILS MY NOTES SPRECALC8 6.2.067. PREVIOUS ANSWERS ASK YOUR TEACHER PRACTICE ANOTHER elevation is found to be 36∘36^{\circ}36∘. Estimate the height of the mountain (in ft ). (Round your answer to the nearest foot.) 4477 xftx \mathrm{ft}xftNeed Help? Read It Watch it

Problem 226

Find sin⁡θ\sin \thetasinθ, where θ\thetaθ is the angle shown. Give an exact value, not a decimal approximation. sin⁡θ=\sin \theta=sinθ= □\square□

Problem 227

Problem 228

Problem 229

4. From the top of the tower 30 m height a man is observing the base of a tree at an angle of depression measuring 30∘30^{\circ}30∘. Find the distance between the tree and the tower.

Problem 230

6. A ladder is leaning against a vertical wall makes an angle of 50∘50^{\circ}50∘ with the ground. The foot of the ladder is 3 ft from the wall. Find the length of ladder.

Problem 231

Problem 232

Find the angle of bend aaa in a right triangle where the rise is 14" and the base is 34". Choices: 22.38deg22.38 \mathrm{deg}22.38deg, 21.25deg21.25 \mathrm{deg}21.25deg, 42.97deg42.97 \mathrm{deg}42.97deg, 37.65deg37.65 \mathrm{deg}37.65deg.

Problem 233

Find the hypotenuse of a right triangle with a 32∘32^{\circ}32∘ angle and an opposite side of 12. Round to the nearest hundredth.

Problem 234

Problem 235

If a tree has a height of 165 feet, what would be the angle of elevation from level ground measured from 95 feet away? Round your answer to the nearest tenth of a degree.

Problem 236

Problem 237

Use △DEF\triangle D E F△DEF to calculate exact values of sine, cosine, and tangent for 30∘30^{\circ}30∘ and 60∘60^{\circ}60∘.

Problem 238

Find the exact value of cos⁡G\cos{G}cosG in simplest radical form.cos⁡G=\cos{G} =cosG=Answer Attempt 1 out of 2 Submit Answer

Problem 239

3. 5. 6. 4.

Problem 240

Find the length of an escalator at a 35∘35^{\circ}35∘ angle that covers a vertical distance of 16 feet. Round to 1 decimal place.

Problem 241

Find the angle θ\thetaθ made by a 67-foot rope anchored 37.2 feet from a vertical pole using tan⁡(θ)=37.267\tan(\theta) = \frac{37.2}{67}tan(θ)=6737.2​.

Problem 242

Find the height of a hill with a road at a 5.4∘5.4^{\circ}5.4∘ angle and a length of 3.1 miles. Round to 2 decimal places.

Problem 243

Find the distance from a rock to a tree, given a stake 24.0 yards north of the rock with a bearing of S16.0∘WS 16.0^{\circ} WS16.0∘W. Round to the nearest tenth of a yard.

Problem 244

Evaluate $\cos \frac{\pi}{4}$ using special right triangles and simplify your answer.

Evaluate $\cot \frac{\pi}{3}$ using special right triangles. Simplify your answer with integers or fractions.

Find the six trigonometric functions for angle $\theta$ in a right triangle where the opposite side is 16 and adjacent side is 12.

Dalam segitiga $PQR$ dengan $\tan \theta=\frac{5}{12}$ , cari nilai $\sin \alpha$ terkait $\alpha$ dan $\theta$ .

Evaluate the expression using special right triangles:
$\frac{\sec ^{2} \frac{\pi}{3}+\tan ^{2} \frac{\pi}{4}}{\cot ^{2} \frac{\pi}{6}}=$
Simplify your answer, including radicals.

If $\sec \theta=6$ , find $\csc \theta$ , $\cot \theta$ , $\sin \theta$ , $\cos \theta$ , and $\tan \theta$ .

Find the sine of $\angle T$ .
Write your answer in simplified, rationalized form. Do not round. $\sin (T)=$ $\square$

Solve for $x$ in the triangle. Round your answer to the nearest tenth. $x=$

A night triangle has side lengths 5,12 , and 13 as shown below. Use these lengths to find $\cos B, \tan B$ , and $\sin B$ . $\begin{array}{l} \cos B= \\ \tan B= \\ \sin B= \end{array}$ $\square$ $\square$ $\square$

A right triangle has side lengths 5,12 , and 13 as shown below. Use these lengths to find $\tan M, \sin M$ , and $\cos M$ . $\begin{array}{l} \tan M=\square \\ \sin M=\square \\ \cos M=\square \end{array}$

Select the correct answer.
In $\triangle A B C, \angle A$ is a right angle. What is the value of $y$ ? A. $7 \sin \frac{\pi}{6}$ B. $7 \cos \frac{\pi}{6}$ C. $7 \tan \frac{\pi}{6}$ D. 7

Select the correct answer.
Given a right triangle, if $\tan \theta=\frac{(3)}{(4)}$ , what is the length of the side adjacent to $\angle \theta ?$ A. 3 B. 4 C. 5 D. 75

Type the correct answer in the box. Round your answer to the nearest integer.
A train traveled a distance of 1 mile, or 5,280 feet, while climbing a hill at an angle of $5^{\circ}$ .
The vertical height that the train climbed is approximately $\square$ feet.

For the triangle shown below, use your calculator to solve for the missing sides and angles. $\theta=$ $\square$ degrees $f=$ $\square$ $e=$ $\square$ Round your answers to two decimal places. Question Help: Video 1 Video 2

3. Find the sine of angle A. Give your answer as a fraction in simplest form. $\operatorname{Sin} A=$ $\qquad$ I - Choose the correct answer - $\qquad$
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7. Nate is in a meadow standing exactly 185 ft from the base of a mountain. He sees someone climbing the mountain in his binoculars. His eyes are 6 ft above the ground, and is angle of elevation is $10^{\circ}$ . How far above the ground is the climber?

Gina and Hone are on opposite sides of a tower. Gina is 20 m away with an angle of elevation of $53^{\circ}$ . Hone's angle is $37^{\circ}$ . Find Hone's distance from the tower.

Peter sees a flag-pole $6 \mathrm{~m}$ away. Angle of depression is $65^{\circ}$ , and elevation is $47^{\circ}$ . Find the height.

14. [0/1 Points]
DETAILS MY NOTES SPRECALC8 6.2.067. PREVIOUS ANSWERS ASK YOUR TEACHER PRACTICE ANOTHER elevation is found to be $36^{\circ}$ . Estimate the height of the mountain (in ft ). (Round your answer to the nearest foot.) 4477 $x \mathrm{ft}$
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Find $\sin \theta$ , where $\theta$ is the angle shown. Give an exact value, not a decimal approximation. $\sin \theta=$ $\square$

4. From the top of the tower 30 m height a man is observing the base of a tree at an angle of depression measuring $30^{\circ}$ . Find the distance between the tree and the tower.

6. A ladder is leaning against a vertical wall makes an angle of $50^{\circ}$ with the ground. The foot of the ladder is 3 ft from the wall. Find the length of ladder.

Find the angle of bend $a$ in a right triangle where the rise is 14" and the base is 34". Choices: $22.38 \mathrm{deg}$ , $21.25 \mathrm{deg}$ , $42.97 \mathrm{deg}$ , $37.65 \mathrm{deg}$ .

Find the hypotenuse of a right triangle with a $32^{\circ}$ angle and an opposite side of 12. Round to the nearest hundredth.

Use $\triangle D E F$ to calculate exact values of sine, cosine, and tangent for $30^{\circ}$ and $60^{\circ}$ .

Find the exact value of $\cos{G}$ in simplest radical form.
$\cos{G} =$
Answer Attempt 1 out of 2 Submit Answer

Find the length of an escalator at a $35^{\circ}$ angle that covers a vertical distance of 16 feet. Round to 1 decimal place.

Find the angle $\theta$ made by a 67-foot rope anchored 37.2 feet from a vertical pole using $\tan(\theta) = \frac{37.2}{67}$ .

Find the height of a hill with a road at a $5.4^{\circ}$ angle and a length of 3.1 miles. Round to 2 decimal places.

Find the distance from a rock to a tree, given a stake 24.0 yards north of the rock with a bearing of $S 16.0^{\circ} W$ . Round to the nearest tenth of a yard.

Solve the right triangle $A B C$ for all missing parts. Express angles in decimal degrees. $\mathrm{A}=22^{\circ} 16^{\prime}, \mathrm{c}=21.75 \mathrm{~m}$ $B \approx$ $\square$ - (Round to the nearest hundredth as needed.)

Find the length of the rafter shown.
The length of the rafter is $\square$ in. (Round to the nearest inch as needed.)

Find the value of $\sin W$ rounded to the nearest hundredth, if necessary.

Solve for $x$ . Round to the nearest tenth, if necessary. $52$ $18^\circ$ $x$ D E F

Find $\cos \theta$ if $\tan \theta=\frac{4}{3}$ . Options: $\frac{3}{5}$ , $\frac{3}{4}$ , $\frac{5}{3}$ , $\frac{4}{5}$ .

Solve the right triangle.
$Q$ $6.1$ $P$ $41^\circ$ $R$
Write your answers as integers or as decimals rounded to the nearest tenth. $QR =$ $PR =$ $m\angle Q =$

A tower is located 239.1 ft from a building. From a window in the building, a person measures an angle of elevation of $42^{\circ}$ to the top of the building, and an angle of depression of $16.8^{\circ}$ to the base of the tower. Find the height of the tower. $\qquad$ ft

Use the image to answer the question.
2 ft.
Ramp up to the house
$20^\circ$
Tyrese is building a ramp up to his home. He knows the height of the ramp is 2 feet. If the angle of elevation of the ramp is $20^\circ$ , how long does the ramp have to be?
(1 point)

Find the exact value of $\tan J$ in simplest radical form.
Answer Attempt 1 out of 2 $\tan J=$ $\square$ Submit Answer $\square$

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Find the exact value of $\sin M$ in simplest radical form.
Answer Attempt 1 out of 2 $\sin M=$ $\square$ Submit Answer

$2$ X $10$ Y $5$ $5\sqrt{3}$ Z \sin{X} = \text{______}

Type decimal answer to the nearest tenth place Find DF to the nearest tenth. $10.0$ $43.6^\circ$

1) Practice $3$ $5$ $4$ B C $\sin(\angle A) =$ 2) $8$ $17$ C A $\sin(\angle A) =$ 3) A $20$ $29$ $21$ C B $\sin(\angle A) =$ 4) P $8$ $10$ N $6$ M $\sin(\angle P) =$

Basic Trig: Cosine 8) 5 9) 29 4 21 $\cos(\angle A) =$ $\cos(\angle A) =$ 10) 17 8 $\cos(\angle B) =$ Basic Trig: Tangent Practice 11) 5 12) 17 3 8 4 $\tan(\angle A) =$ $\tan(\angle A) =$

Find the tangent of $\angle B$ .
$10$ $\sqrt{14}$
Write your answer in simplified, rationalized form. Do not round.
$\tan(B) =$

$x =$ $9$ $65^\circ$ $x$

Solve for $x$ in the triangle. Round your answer to the nearest tenth. $55^{\circ}$ $12$ $x$

A kite flying in the air has an 86-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is $53^\circ$ . Find the height of the kite. Round your answer to the nearest tenth. 86 $53^\circ$ ft

Find x. Round your answer to the nearest tenth of a degree. $x = \Box^{\circ}$ 13 9

(1) $a=$

Find $\tan A$ in triangle $ABC$ (right angle at $C$ ) with sides $a=6$ and $b=7$ . Provide exact answers.

Find $\sin A$ for right triangle $\mathrm{ABC}$ with sides $a=5$ and $b=3$ . Exact answers only.

Find $\cos A$ for a right triangle with sides $a=5$ and $b=2$ . Provide the exact answer with a rational denominator.

Find the value of $\cot A$ in triangle $ABC$ where $b=5$ and $c=6$ . Provide exact answers with rational denominators.

Find the length of a guy wire attached 10 ft from the top of a 230 ft tower at a $32^{\circ}$ angle. Round to the nearest tenth.

Find $\csc B$ for a right triangle with sides $a=5$ and $b=6$ . Provide exact answers with rational denominators.