Pythagorean Theorem

Problem 101

The length of one leg of a right triangle is 7 cm more than that of the other leg. The length of the hypotenuse is 3 cm more than double that of the shorter leg. Find the lengths of each of the three sides.

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Problem 102

For the following right triangle, find the side length $x$ .

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Problem 103

Find the hypotenuse of a right triangle with sides 14 and 11.5. Round your answer to the nearest tenth.

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Problem 104

Find the shortest distance between Stan and Wei, given Jeff's locations: 12 miles east of Stan and 16 miles north of Wei.

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Problem 105

Find the diagonal length of a monitor with dimensions 24 inches (length) and 18 inches (height) to the nearest inch. Use $d = \sqrt{24^2 + 18^2}$ .

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Problem 106

اوجد كل المثلثات الفيثاغورية البدانية التي طول احد الساقين فيها يساوي 80 .

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Problem 107

Answer Attempt 1 out of 2
Estimated length of $\overline{Q S}=4.3 \mathrm{~cm}$ The actual length of $\overline{Q S}=$ $\square$ cm (round to 3 decimal places)

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Problem 108

Answer Attempt 2 out of 2
Estimated length of $\overline{Q S}=4.3 \mathrm{~cm}$ The actual length of $\overline{Q S}=$ $\square$ cm (round to 3 decimal places)

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Problem 109

Answer Attempt 1 out of 2
Estimated length of $\overline{A B}=9.2 \mathrm{~cm}$ The actual length of $\overline{A B}=$ $\square$ cm (round to 3 decimal places)

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Problem 110

Answer Attempt 1 out of 2 Estimated length of $\overline{W X}=7.5 \mathrm{~cm}$ The actual length of $\overline{W X}=$ $\square$ cm (round to 3 decimal places)

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Problem 111

The length of the longer leg of a right triangle is 19 cm more than five times the length of the shorter leg. The length of the hypotenuse is 20 cm more than five times the length of the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg: $\square$ cm
Length of the longer leg: $\square$ cm Length of the $\square$ cm hypotenuse: 5

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Problem 112

The areas of the squares adjacent to two sides of a right triangle are shown below.
What is the area of the square adjacent to the third side of the triangle? $\square$ units ${ }^{2}$

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Problem 113

Two congruent squares are shown in Figures 1 and 2 below.
Figure 1
Figure 2 se the drop-down menus to complete the proof of the Pythagorean Theorem using the figures. lick the arrows to choose an answer from each menu.
The combined area of the shaded triangles in Figure 1 is Choose... the combined area of the shaded triangles in Figure 2. The area of the unshaded square in Figure 1 can be represented by Choose... $\square$ - The combined area of the two unshaded squares in Figure 2 can be represented by Choose... . The areas of the squares in Figure 1 and Figure ress

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Problem 114

Find $x$ in a right triangle with sides 10 and 11 using the Pythagorean theorem.

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Problem 115

Calculate the hypotenuse of a right triangle with sides 8 and 10. Round your answer to 2 decimal places.

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Problem 116

In a right triangle with sides 7 and 16, calculate the length of $x$ . $x=$

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Problem 117

How far does a catcher throw from home plate to second base in a 60-foot diamond? Use the distance formula: $d = \sqrt{(60^2 + 60^2)}$ .

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Problem 118

Check if the triangle with vertices B(-1,5), A(2,3), and C(0,0) is a right triangle using the distances.

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Problem 119

Imagine you need to purchase a laptop bag for your 14 -inch laptop. The only problem is you don't have your laptop with you, and it sure would be frustrating to buy a bag only to realize that your laptop doesn't quite fit.
You recall laptop computers are measured according to the diagonals of their screens, and you remember your 14 -inch laptop has a screen that is 8 inches tall. How wide is the screen?
Exact Answer (written as a simpified radical): $\square$ in.
Approximate (decimal) Answer: $\square$ in. Give your approximate answer accurate to 2 decimal places.

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Problem 120

Find the missing side.
Round to the nearest tent

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Problem 121

Find the missing side.

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Problem 122

A 10 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth. $x=$ Question Help: Video

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Problem 123

Question Progress
Homework Progress 屁 43 / 52 Marks
Calculate the length of $A C$ to 1 decimal place in the trapezium below. $\square$ $A C=$ $\square$ 207 cm

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Problem 124

5. Solve for x : 7.64 9.35 8.17 6.22 Clear All

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Problem 125

2. Explain how the diagram demonstrates the Pythagorean Theorem.

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Problem 126

Find the length of the third side. If necessary, round to the nearest tenth.
Answer Attempt 1 out of 2 $\square$ Submit Answer

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Problem 127

In the figure below, find the exact value of $y$ . (Do not approximate your answer.) $y=$ $\square$

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Problem 128

A $10 \mathrm{~m}$ steel plate forms a ramp with a $3 \mathrm{~m}$ clearance. Find the distance $(d)$ from point A to B.

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Problem 129

Brandy's storage unit is 8 ft wide and 17 ft diagonal. Find the length $c$ using $8^2 + c^2 = 17^2$ .

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Problem 130

A 12-foot ladder leans against a wall, 3 feet from the base. How high does it reach? Round to the nearest tenth.

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Problem 131

A catcher throws the ball from home plate to second base. Find the distance, rounding to the nearest tenth. Use $d = \sqrt{90^2 + 90^2}$ .

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Problem 132

Find the width of a 70" TV with a 16:9 aspect ratio. Options: $80.33^{\prime \prime}$ , $39.4^{\prime \prime}$ , $61^{\prime \prime}$ , $44.8^{\prime \prime}$ .

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Problem 133

Find the distance from home plate to second base on a square baseball diamond with 86-foot sides. Express in radical form and decimal.

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Problem 134

POSSIBLE POINTS
A diagram demonstrates the Pythagorean Theorem, which states that for a right triangle with legs $a$ and $b$ and hypotenuse $c, a^{2}+b^{2}=c^{2}$ .
How are the squares in the diagram related to the equation? The number of unit squares in each square is equal to the adjacent side length. The square of the sum of the legs equals the square of the hypotenuse. The square shapes represent the squares of the side lengths, and the sum of the areas of the two smaller squares equals the area of the larger square. The squares represent the side lengths of the triangle. The sum of the side lengths of the legs equals the length of the hypotenuse. The square of the sum of the lengths of the sides of the triangle equals the number of unit squares in all the squares.

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Problem 135

The Varners live on a corner lot. Often, children cut across their lot to save walking distance. The diagram to the right represents the corner lot. The children's path is represented by a dashed line. Approximate the walking distance that is saved by cutting across their property instead of walking around the lot.

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Problem 136

at?
C (2.2.34), (2.2.29) b. $(-3,-3),(-3,3)$ F. $(2,-4),(2, *)$

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Problem 137

Find the length of the missing leg in a right triangle with hypotenuse 10 units and one leg 6 units.

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Problem 138

Find the missing side of a right triangle with sides 6.5 and 4. Round your answer to the nearest hundredth. Use $a^2 + b^2 = c^2$ .

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Problem 139

Find the length of the banister for a staircase that rises $15 \mathrm{ft}$ and spans $20 \mathrm{ft}$ . Round to the nearest tenth.

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Problem 140

Leave your answers in simplest radical form. 2)

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Problem 141

3. Find the distance between the two points using the Pythagorean Theorem: A. $\sqrt{82}$ B. $\sqrt{5}$ C. $\sqrt{26}$ D. $\sqrt{85}$
Nistance between the two points using the Pythagorean Theorem:

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Problem 142

4. Find the distance between the two points using the Pythagorean Theorem: A. $\sqrt{82}$ B. $\sqrt{5}$ C. $\sqrt{26}$ D. $\sqrt{85}$

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Problem 143

2. Use the Pythagorean Theorem to find the distance between the two points. Round your answer to th

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Problem 144

2. Use the Pythagorean Theorem to find the distance between

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Problem 145

Janet and Michelle walk from the same point. When $10 \mathrm{~km}$ apart, Michelle walked $2 \mathrm{~km}$ more. How far did Michelle walk? $12 \mathrm{~km}$ $6 \mathrm{~km}$ $8 \mathrm{~km}$ $10 \mathrm{~km}$

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Problem 146

$3$ mi. $a$ $2$ mi. What is the perimeter? If necessary, round to the nearest tenth.

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Problem 147

Find the hypotenuse of a right triangle with sides 24 and 7 using the Pythagorean theorem: $c^2 = 24^2 + 7^2$ .

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Problem 148

Find side $c$ in right triangle $ABC$ with $a=8$ and $b=15$ using the Pythagorean theorem. Then, find trig functions for angle B.

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Problem 149

Find the unknown side length $b$ in triangle $ABC$ using $a=10$ and $c=20$ . Then calculate the six trig functions for angle B.

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Problem 150

18 Mark for Review
An isosceles right triangle has a hypotenuse of length 58 inches. What is the perimeter, in inches, of this triangle? (A) $29 \sqrt{2}$

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Problem 151

In a right triangle, one leg is 8 and the hypotenuse is 11. Find the length of the other leg $x$ .

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Problem 152

Jenifer's kite string is 19 ft long and she's 12 ft from the tree. Find the ladder length needed to reach the kite: $l = \sqrt{19^2 - 12^2}$ . Enter your answer in radical form.

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Problem 153

Find a value of the Pythagorean triple using $x=18$ and $y=9$ with the identity $(x^{2}+y^{2})^{2}=(x^{2}-y^{2})^{2}+(2xy)^{2}$ . Options: 162, 81, 324, 729.

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Problem 154

A stuntman runs at $5.26 \mathrm{~m/s}$ . Can he jump $7.60 \mathrm{~m}$ horizontally and $4.70 \mathrm{~m}$ down?

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Problem 155

In the opposite figure : $x + y + z = \dots$ (a) 15 (b) 18.2 (c) 22 (d) 22.2 9cm. 7cm. 12cm. $x$ cm. $y$ cm.

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Problem 156

Find the length of the third side. If necessary, round to the nearest tenth. 6 8

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Problem 157

If you place a 40-foot ladder against the top of a building and the bottom of the ladder is 17 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot. Answer Attempt 1 out of 3 ft Submit Answer

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Problem 158

If you place a 24 -foot ladder against the top of a 20 -foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.
Answer

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Problem 159

The area of a rectangle is 99 square units. Its width measures 11 units. Find the length of its diagonal. Round to the nearest tenth of a unit.

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Problem 160

If you place a 23 -foot ladder against the top of a building and the bottom of the ladder is 11 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.

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Problem 161

Find the missing side in right triangle $ABC$ with $a=5$ and $b=12$ using the Pythagorean theorem. Then, calculate the six trigonometric functions for angle $B$ .

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Problem 162

Find the unknown side of right triangle $ABC$ with $a=7$ and $c=14$ . Then calculate the six trig functions for angle B.

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Problem 163

In triangle $ABC$ , with $a=7$ and $c=14$ , find side $b$ using the Pythagorean theorem and calculate $\sin B$ and $\cos B$ .

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Problem 164

Find the unknown side length of right triangle $ABC$ using the Pythagorean theorem, given $a=6$ and $c=7$ . Then, calculate the trig functions for angle B, rationalizing denominators if needed.

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Problem 165

What does the law of cosines reduce to when dealing with a right triangle? A. The Pythagorean theorem B. The formula for a triangle's area C. The formula for a triangle's area D. The law of sines

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Problem 166

$20 \cdot 50 + 16 \cdot 50$
$h$
$hyp$
$20$
$\frac{1}{2}$
$(16)(18.3)$
$8$
$h^2 + 8^2 = 20^2$
$h^2 + 64 = 400$
$-64 -64$
$h^2 = 336$
$h = 18.3$

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Problem 167

Find the hypotenuse of a right triangle with legs $a=16$ and $b=30$ . What is its length in units?

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Problem 168

Check if the triangle with sides 2, 5, and 6 is a right triangle and find the hypotenuse if it is.

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Problem 169

Check if the triangle with sides 27, 36, and 45 is a right triangle and find the hypotenuse if it is.

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Problem 170

Find the hypotenuse of a right triangle with legs $a=20$ and $b=48$ .

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Problem 171

Find leg $x$ in a right triangle with sides 18 and 9. $x$ is a leg, not the hypotenuse.

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Problem 172

Find the leg length $x$ in a right triangle with one leg 18 and hypotenuse 9.

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Problem 173

Find the leg $x$ of a right triangle with hypotenuse 18 and other leg 9. Provide the exact value. $x=$

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Problem 174

Find the distance you need to ride east before heading north to reach your friend's house, given a $10.0 \mathrm{~km}$ distance and $6.0 \mathrm{~km}$ north.

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Problem 175

Find $b$ in the Pythagorean theorem $3^2 + b^2 = 5^2$ . Round your answer to two decimal places.

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Problem 176

Find $c$ in a right triangle where $a=13$ and $b=12$ using the Pythagorean theorem.

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Problem 177

Find the distance between the two points in simplest radical form. Answer Attempt 2 out of 2

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Problem 178

Question Use the Pythagorean Theorem to find the length of the leg in the triangle below.

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Problem 179

The length of one leg of a right triangle is 6 cm and the length of the hypotenuse is $2 \sqrt{14} \mathrm{~cm}$ . Which measure represents the length of the other leg? $2 \sqrt{23} \mathrm{~cm}$ $2 \sqrt{5} \mathrm{~cm}$ $4 \sqrt{7} \mathrm{~cm}$ 4 cm

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Problem 180

1. The area of the square on Is the triangle a right tria a)

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Problem 181

se the Pythagorean theorem to find the unknown side of the right triangle.
Hypotenuse length = $\square$ (Simplify your answer. Type exact answers, using radicals as needed)

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Problem 182

```latex \text{Find the missing lengths } X \text{ and } Y. \text{ Round your answers to the nearest hundredth.} \\ \text{Given:} \\ \text{Triangle 1:} \\ \text{Hypotenuse } = 12, \text{ one leg } = 4, \text{ other leg } = X \\ \text{Triangle 2:} \\ \text{Hypotenuse } = 33, \text{ one leg } = 21, \text{ other leg } = Y \\ \text{Solve and round your answers to the nearest tenth. Must show your work to get full point.} ```

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Problem 183

Find leg $x$ in a right triangle with hypotenuse 18 and other leg 9. Round to the nearest tenth.

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Problem 184

A TV has a 37-inch diagonal and is 23 inches tall. What is the width of the screen? Round to the nearest tenth.

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Problem 185

Find the distance from Bangtown to Bongtown, given Bingtown is 40 miles north of Bongtown and 75 miles west of Bingtown.

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Problem 186

In a right triangle, $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse. If $a=6.5$ meters and $b=7$ meters, what is $c$ ? If necessary, round to the nearest tenth. $\square$ meters

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Problem 187

Video
In a right triangle, $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse. If $a=2$ meters and $b=6$ meters, what is $c$ ? If necessary, round to the nearest tenth. $c=$ $\square$ meters Submit

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Problem 188

In a right triangle, $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse. If $a=3.4$ kilometers and $b=1.8$ kilometers, what is $c$ ? If necessary, round to the nearest tenth. $c=$ $\square$ kilometers

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Problem 189

A building's shadow is 32 m, and the distance from the top to the shadow's tip is 35 m. Find the building's height.

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Problem 190

A building's shadow is 32 m long, and the distance from the top to the shadow's tip is 37 m. Find the building's height.

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Problem 191

A kite has a 12-ft line and an 11-ft shadow. Find the height of the kite, rounding to the nearest tenth.

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Problem 192

A triangle has sides with lengths of 74 yards, 48 yards, and 55 yards. Is it a right triangle? yes no
Submit

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Problem 193

Find the height of the tree shown to the right.

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Problem 194

Progress: Question ID: 109878
The movement of the progress bar moy be uneven because questions can be worth more or less (including zero) depenaling on your answer. A camper attaches a rope to the top of her tent to give it more support. She stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. About how tall is her tent? 4.5 feet 6 feet 5.3 feet

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Problem 195

Use the information given in the figure to find the length $K N$ . If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.

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Problem 196

Home > CCA2 > Chapter $2>$ Lesson 2.1.2 > Problem 2-21
2-21. Plot each pair of points and find the distance between them. Give answers in both square-root form and as decimal approximations. $\square$ $\square$ Hint: Draw a right triangle with the hypotenuse segment connecting the given points. Recall the Pythagorean Theorem. Find the difference between the $x$ - and $y$ coordinates, respectively. Square these values, add them, and find the square root of this value. a. $(3,-6)$ and $(-2,5)$ b. $(5,-8)$ and $(-3,1)$ c. $(0,5)$ and $(5,0)$ d. Write the distance you found in $\square$ DAnswer (a): part (c) in simplified square-root $\sqrt{146} \approx 12.1$ form. $\square$ (2Hint (d): Rewrite $\sqrt{50}$ as $\sqrt{25} \cdot \sqrt{2}$ . Which factor can be simplified further?

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Problem 197

In the figure below, find the exact value of $z$ . (Do not approximate your answer.) $z=$

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Problem 198

In the sentence "She calculated the hypotenuse of the triangle using the measurements of the other two sides," which word or phrase is the most helpfull context clue to figure out what the word hypotenuse means?
Select one of four
Triangle Calculated
Measurements Other two sides

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Problem 199

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.

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Problem 200

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary. Previous

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1 2 3

Pythagorean Theorem

Problem 101

The length of one leg of a right triangle is 7 cm more than that of the other leg. The length of the hypotenuse is 3 cm more than double that of the shorter leg. Find the lengths of each of the three sides.

Problem 102

For the following right triangle, find the side length xxx.

Problem 103

Find the hypotenuse of a right triangle with sides 14 and 11.5. Round your answer to the nearest tenth.

Problem 104

Find the shortest distance between Stan and Wei, given Jeff's locations: 12 miles east of Stan and 16 miles north of Wei.

Problem 105

Find the diagonal length of a monitor with dimensions 24 inches (length) and 18 inches (height) to the nearest inch. Use d=242+182d = \sqrt{24^2 + 18^2}d=242+182​.

Problem 106

اوجد كل المثلثات الفيثاغورية البدانية التي طول احد الساقين فيها يساوي 80 .

Problem 107

Answer Attempt 1 out of 2Estimated length of QS‾=4.3 cm\overline{Q S}=4.3 \mathrm{~cm}QS​=4.3 cm The actual length of QS‾=\overline{Q S}=QS​= □\square□ cm (round to 3 decimal places)

Problem 108

Answer Attempt 2 out of 2Estimated length of QS‾=4.3 cm\overline{Q S}=4.3 \mathrm{~cm}QS​=4.3 cm The actual length of QS‾=\overline{Q S}=QS​= □\square□ cm (round to 3 decimal places)

Problem 109

Answer Attempt 1 out of 2Estimated length of AB‾=9.2 cm\overline{A B}=9.2 \mathrm{~cm}AB=9.2 cm The actual length of AB‾=\overline{A B}=AB= □\square□ cm (round to 3 decimal places)

Problem 110

Answer Attempt 1 out of 2 Estimated length of WX‾=7.5 cm\overline{W X}=7.5 \mathrm{~cm}WX=7.5 cm The actual length of WX‾=\overline{W X}=WX= □\square□ cm (round to 3 decimal places)

Problem 111

Problem 112

The areas of the squares adjacent to two sides of a right triangle are shown below.What is the area of the square adjacent to the third side of the triangle? □\square□ units 2{ }^{2}2

Problem 113

Problem 114

Find xxx in a right triangle with sides 10 and 11 using the Pythagorean theorem.

Problem 115

Calculate the hypotenuse of a right triangle with sides 8 and 10. Round your answer to 2 decimal places.

Problem 116

In a right triangle with sides 7 and 16, calculate the length of xxx. x=x= x=

Problem 117

How far does a catcher throw from home plate to second base in a 60-foot diamond? Use the distance formula: d=(602+602)d = \sqrt{(60^2 + 60^2)}d=(602+602)​.

Problem 118

Check if the triangle with vertices B(-1,5), A(2,3), and C(0,0) is a right triangle using the distances.

Problem 119

Problem 120

Find the missing side.Round to the nearest tent

Problem 121

Find the missing side.

Problem 122

A 10 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth. x=x=x= Question Help: Video

Problem 123

Question ProgressHomework Progress 屁 43 / 52 MarksCalculate the length of ACA CAC to 1 decimal place in the trapezium below. □\square□ AC=A C=AC= □\square□ 207 cm

Problem 124

5. Solve for x : 7.64 9.35 8.17 6.22 Clear All

Problem 125

2. Explain how the diagram demonstrates the Pythagorean Theorem.

Problem 126

Find the length of the third side. If necessary, round to the nearest tenth.Answer Attempt 1 out of 2 □\square□ Submit Answer

Problem 127

In the figure below, find the exact value of yyy. (Do not approximate your answer.) y=y=y= □\square□

Problem 128

A 10 m10 \mathrm{~m}10 m steel plate forms a ramp with a 3 m3 \mathrm{~m}3 m clearance. Find the distance (d)(d)(d) from point A to B.

Problem 129

Brandy's storage unit is 8 ft wide and 17 ft diagonal. Find the length ccc using 82+c2=1728^2 + c^2 = 17^282+c2=172.

Problem 130

A 12-foot ladder leans against a wall, 3 feet from the base. How high does it reach? Round to the nearest tenth.

Problem 131

A catcher throws the ball from home plate to second base. Find the distance, rounding to the nearest tenth. Use d=902+902d = \sqrt{90^2 + 90^2}d=902+902​.

Problem 132

Find the width of a 70" TV with a 16:9 aspect ratio. Options: 80.33′′80.33^{\prime \prime}80.33′′, 39.4′′39.4^{\prime \prime}39.4′′, 61′′61^{\prime \prime}61′′, 44.8′′44.8^{\prime \prime}44.8′′.

Problem 133

Find the distance from home plate to second base on a square baseball diamond with 86-foot sides. Express in radical form and decimal.

Problem 134

Problem 135

Problem 136

at?C (2.2.34), (2.2.29) b. (−3,−3),(−3,3)(-3,-3),(-3,3)(−3,−3),(−3,3) F. (2,−4),(2,∗)(2,-4),(2, *)(2,−4),(2,∗)

Problem 137

Find the length of the missing leg in a right triangle with hypotenuse 10 units and one leg 6 units.

Problem 138

Find the missing side of a right triangle with sides 6.5 and 4. Round your answer to the nearest hundredth. Use a2+b2=c2a^2 + b^2 = c^2a2+b2=c2.

Problem 139

Find the length of the banister for a staircase that rises 15ft15 \mathrm{ft}15ft and spans 20ft20 \mathrm{ft}20ft. Round to the nearest tenth.

Problem 140

Leave your answers in simplest radical form. 2)

Problem 141

3. Find the distance between the two points using the Pythagorean Theorem: A. 82\sqrt{82}82​ B. 5\sqrt{5}5​ C. 26\sqrt{26}26​ D. 85\sqrt{85}85​Nistance between the two points using the Pythagorean Theorem:

Problem 142

4. Find the distance between the two points using the Pythagorean Theorem: A. 82\sqrt{82}82​ B. 5\sqrt{5}5​ C. 26\sqrt{26}26​ D. 85\sqrt{85}85​

For the following right triangle, find the side length $x$ .

Find the diagonal length of a monitor with dimensions 24 inches (length) and 18 inches (height) to the nearest inch. Use $d = \sqrt{24^2 + 18^2}$ .

Answer Attempt 1 out of 2
Estimated length of $\overline{Q S}=4.3 \mathrm{~cm}$ The actual length of $\overline{Q S}=$ $\square$ cm (round to 3 decimal places)

Answer Attempt 2 out of 2
Estimated length of $\overline{Q S}=4.3 \mathrm{~cm}$ The actual length of $\overline{Q S}=$ $\square$ cm (round to 3 decimal places)

Answer Attempt 1 out of 2
Estimated length of $\overline{A B}=9.2 \mathrm{~cm}$ The actual length of $\overline{A B}=$ $\square$ cm (round to 3 decimal places)

Answer Attempt 1 out of 2 Estimated length of $\overline{W X}=7.5 \mathrm{~cm}$ The actual length of $\overline{W X}=$ $\square$ cm (round to 3 decimal places)

The areas of the squares adjacent to two sides of a right triangle are shown below.
What is the area of the square adjacent to the third side of the triangle? $\square$ units ${ }^{2}$

Find $x$ in a right triangle with sides 10 and 11 using the Pythagorean theorem.

In a right triangle with sides 7 and 16, calculate the length of $x$ . $x=$

How far does a catcher throw from home plate to second base in a 60-foot diamond? Use the distance formula: $d = \sqrt{(60^2 + 60^2)}$ .

Find the missing side.
Round to the nearest tent

A 10 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth. $x=$ Question Help: Video

Question Progress
Homework Progress 屁 43 / 52 Marks
Calculate the length of $A C$ to 1 decimal place in the trapezium below. $\square$ $A C=$ $\square$ 207 cm

Find the length of the third side. If necessary, round to the nearest tenth.
Answer Attempt 1 out of 2 $\square$ Submit Answer

In the figure below, find the exact value of $y$ . (Do not approximate your answer.) $y=$ $\square$

A $10 \mathrm{~m}$ steel plate forms a ramp with a $3 \mathrm{~m}$ clearance. Find the distance $(d)$ from point A to B.

Brandy's storage unit is 8 ft wide and 17 ft diagonal. Find the length $c$ using $8^2 + c^2 = 17^2$ .

A catcher throws the ball from home plate to second base. Find the distance, rounding to the nearest tenth. Use $d = \sqrt{90^2 + 90^2}$ .

Find the width of a 70" TV with a 16:9 aspect ratio. Options: $80.33^{\prime \prime}$ , $39.4^{\prime \prime}$ , $61^{\prime \prime}$ , $44.8^{\prime \prime}$ .

at?
C (2.2.34), (2.2.29) b. $(-3,-3),(-3,3)$ F. $(2,-4),(2, *)$

Find the missing side of a right triangle with sides 6.5 and 4. Round your answer to the nearest hundredth. Use $a^2 + b^2 = c^2$ .

Find the length of the banister for a staircase that rises $15 \mathrm{ft}$ and spans $20 \mathrm{ft}$ . Round to the nearest tenth.

3. Find the distance between the two points using the Pythagorean Theorem: A. $\sqrt{82}$ B. $\sqrt{5}$ C. $\sqrt{26}$ D. $\sqrt{85}$
Nistance between the two points using the Pythagorean Theorem:

4. Find the distance between the two points using the Pythagorean Theorem: A. $\sqrt{82}$ B. $\sqrt{5}$ C. $\sqrt{26}$ D. $\sqrt{85}$

Janet and Michelle walk from the same point. When $10 \mathrm{~km}$ apart, Michelle walked $2 \mathrm{~km}$ more. How far did Michelle walk? $12 \mathrm{~km}$ $6 \mathrm{~km}$ $8 \mathrm{~km}$ $10 \mathrm{~km}$

$3$ mi. $a$ $2$ mi. What is the perimeter? If necessary, round to the nearest tenth.

Find the hypotenuse of a right triangle with sides 24 and 7 using the Pythagorean theorem: $c^2 = 24^2 + 7^2$ .

Find side $c$ in right triangle $ABC$ with $a=8$ and $b=15$ using the Pythagorean theorem. Then, find trig functions for angle B.

Find the unknown side length $b$ in triangle $ABC$ using $a=10$ and $c=20$ . Then calculate the six trig functions for angle B.

18 Mark for Review
An isosceles right triangle has a hypotenuse of length 58 inches. What is the perimeter, in inches, of this triangle? (A) $29 \sqrt{2}$

In a right triangle, one leg is 8 and the hypotenuse is 11. Find the length of the other leg $x$ .

Jenifer's kite string is 19 ft long and she's 12 ft from the tree. Find the ladder length needed to reach the kite: $l = \sqrt{19^2 - 12^2}$ . Enter your answer in radical form.

Find a value of the Pythagorean triple using $x=18$ and $y=9$ with the identity $(x^{2}+y^{2})^{2}=(x^{2}-y^{2})^{2}+(2xy)^{2}$ . Options: 162, 81, 324, 729.

A stuntman runs at $5.26 \mathrm{~m/s}$ . Can he jump $7.60 \mathrm{~m}$ horizontally and $4.70 \mathrm{~m}$ down?

In the opposite figure : $x + y + z = \dots$ (a) 15 (b) 18.2 (c) 22 (d) 22.2 9cm. 7cm. 12cm. $x$ cm. $y$ cm.

If you place a 24 -foot ladder against the top of a 20 -foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.
Answer

Find the missing side in right triangle $ABC$ with $a=5$ and $b=12$ using the Pythagorean theorem. Then, calculate the six trigonometric functions for angle $B$ .

Find the unknown side of right triangle $ABC$ with $a=7$ and $c=14$ . Then calculate the six trig functions for angle B.

In triangle $ABC$ , with $a=7$ and $c=14$ , find side $b$ using the Pythagorean theorem and calculate $\sin B$ and $\cos B$ .

Find the unknown side length of right triangle $ABC$ using the Pythagorean theorem, given $a=6$ and $c=7$ . Then, calculate the trig functions for angle B, rationalizing denominators if needed.

$20 \cdot 50 + 16 \cdot 50$
$h$
$hyp$
$20$
$\frac{1}{2}$
$(16)(18.3)$
$8$
$h^2 + 8^2 = 20^2$
$h^2 + 64 = 400$
$-64 -64$
$h^2 = 336$
$h = 18.3$

Find the hypotenuse of a right triangle with legs $a=16$ and $b=30$ . What is its length in units?

Find the hypotenuse of a right triangle with legs $a=20$ and $b=48$ .

Find leg $x$ in a right triangle with sides 18 and 9. $x$ is a leg, not the hypotenuse.

Find the leg length $x$ in a right triangle with one leg 18 and hypotenuse 9.

Find the leg $x$ of a right triangle with hypotenuse 18 and other leg 9. Provide the exact value. $x=$

Find the distance you need to ride east before heading north to reach your friend's house, given a $10.0 \mathrm{~km}$ distance and $6.0 \mathrm{~km}$ north.