Math / Geometry

QuestionSolve the right triangle for the unknown sides and angles. Round $A=46.2^{\circ}, a=30$ $B=\square{ }^{\circ}$ $b \approx$ $\square$ $c \approx \square$ $\square$ Start over Check

Studdy Solution

STEP 1

1. We have a right triangle.
2. One angle $A = 46.2^\circ$ .
3. The side opposite angle $A$ is $a = 30$ .
4. We need to find angle $B$ , and sides $b$ and $c$ .

STEP 2

1. Find the unknown angle $B$ .
2. Find the hypotenuse $c$ using the sine function.
3. Find the remaining side $b$ using the tangent function.

STEP 3

In a right triangle, the sum of the angles is $180^\circ$ . Since one angle is $90^\circ$ (the right angle), we can find angle $B$ by:
$B = 180^\circ - 90^\circ - A$ $B = 180^\circ - 90^\circ - 46.2^\circ$ $B = 43.8^\circ$

STEP 4

To find the hypotenuse $c$ , we can use the sine function. The sine of angle $A$ is the opposite side over the hypotenuse:
$\sin(A) = \frac{a}{c}$ $\sin(46.2^\circ) = \frac{30}{c}$

STEP 5

Solve for $c$ :
$c = \frac{30}{\sin(46.2^\circ)}$
Calculate $c$ using a calculator:
$c \approx \frac{30}{0.7193}$ $c \approx 41.7$

STEP 6

To find the side $b$ , we can use the tangent function. The tangent of angle $A$ is the opposite side over the adjacent side:
$\tan(A) = \frac{a}{b}$ $\tan(46.2^\circ) = \frac{30}{b}$

STEP 7

Solve for $b$ :
$b = \frac{30}{\tan(46.2^\circ)}$
Calculate $b$ using a calculator:
$b \approx \frac{30}{1.0355}$ $b \approx 28.97$
The unknown sides and angles are:
$B = 43.8^\circ$ $b \approx 28.97$ $c \approx 41.7$

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QuestionSolve the right triangle for the unknown sides and angles. Round $A=46.2^{\circ}, a=30$ $B=\square{ }^{\circ}$ $b \approx$ $\square$ $c \approx \square$ $\square$ Start over Check

Studdy Solution

STEP 1

1. We have a right triangle.
2. One angle $A = 46.2^\circ$ .
3. The side opposite angle $A$ is $a = 30$ .
4. We need to find angle $B$ , and sides $b$ and $c$ .

STEP 2

1. Find the unknown angle $B$ .
2. Find the hypotenuse $c$ using the sine function.
3. Find the remaining side $b$ using the tangent function.

STEP 3

In a right triangle, the sum of the angles is $180^\circ$ . Since one angle is $90^\circ$ (the right angle), we can find angle $B$ by:
$B = 180^\circ - 90^\circ - A$ $B = 180^\circ - 90^\circ - 46.2^\circ$ $B = 43.8^\circ$

STEP 4

To find the hypotenuse $c$ , we can use the sine function. The sine of angle $A$ is the opposite side over the hypotenuse:
$\sin(A) = \frac{a}{c}$ $\sin(46.2^\circ) = \frac{30}{c}$

STEP 5

Solve for $c$ :
$c = \frac{30}{\sin(46.2^\circ)}$
Calculate $c$ using a calculator:
$c \approx \frac{30}{0.7193}$ $c \approx 41.7$

STEP 6

To find the side $b$ , we can use the tangent function. The tangent of angle $A$ is the opposite side over the adjacent side:
$\tan(A) = \frac{a}{b}$ $\tan(46.2^\circ) = \frac{30}{b}$

STEP 7

Solve for $b$ :
$b = \frac{30}{\tan(46.2^\circ)}$
Calculate $b$ using a calculator:
$b \approx \frac{30}{1.0355}$ $b \approx 28.97$
The unknown sides and angles are:
$B = 43.8^\circ$ $b \approx 28.97$ $c \approx 41.7$

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QuestionSolve the right triangle for the unknown sides and angles. Round A=46.2∘,a=30A=46.2^{\circ}, a=30A=46.2∘,a=30 B=□∘B=\square{ }^{\circ}B=□∘ b≈b \approxb≈ □\square□ c≈□c \approx \squarec≈□ □\square□ Start over Check

Studdy Solution

STEP 1

1. We have a right triangle.2. One angle A=46.2∘ A = 46.2^\circ A=46.2∘.3. The side opposite angle A A A is a=30 a = 30 a=30.4. We need to find angle B B B, and sides b b b and c c c.

STEP 2

1. Find the unknown angle B B B.2. Find the hypotenuse c c c using the sine function.3. Find the remaining side b b b using the tangent function.

STEP 3

STEP 4

To find the hypotenuse c c c, we can use the sine function. The sine of angle A A A is the opposite side over the hypotenuse:sin⁡(A)=ac \sin(A) = \frac{a}{c} sin(A)=ca​ sin⁡(46.2∘)=30c \sin(46.2^\circ) = \frac{30}{c} sin(46.2∘)=c30​

STEP 5

Solve for c c c:c=30sin⁡(46.2∘) c = \frac{30}{\sin(46.2^\circ)} c=sin(46.2∘)30​Calculate c c c using a calculator:c≈300.7193 c \approx \frac{30}{0.7193} c≈0.719330​ c≈41.7 c \approx 41.7 c≈41.7

STEP 6

To find the side b b b, we can use the tangent function. The tangent of angle A A A is the opposite side over the adjacent side:tan⁡(A)=ab \tan(A) = \frac{a}{b} tan(A)=ba​ tan⁡(46.2∘)=30b \tan(46.2^\circ) = \frac{30}{b} tan(46.2∘)=b30​

STEP 7

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QuestionSolve the right triangle for the unknown sides and angles. Round $A=46.2^{\circ}, a=30$ $B=\square{ }^{\circ}$ $b \approx$ $\square$ $c \approx \square$ $\square$ Start over Check

1. We have a right triangle.
2. One angle $A = 46.2^\circ$ .
3. The side opposite angle $A$ is $a = 30$ .
4. We need to find angle $B$ , and sides $b$ and $c$ .

1. Find the unknown angle $B$ .
2. Find the hypotenuse $c$ using the sine function.
3. Find the remaining side $b$ using the tangent function.

To find the hypotenuse $c$ , we can use the sine function. The sine of angle $A$ is the opposite side over the hypotenuse:
$\sin(A) = \frac{a}{c}$ $\sin(46.2^\circ) = \frac{30}{c}$

Solve for $c$ :
$c = \frac{30}{\sin(46.2^\circ)}$
Calculate $c$ using a calculator:
$c \approx \frac{30}{0.7193}$ $c \approx 41.7$

To find the side $b$ , we can use the tangent function. The tangent of angle $A$ is the opposite side over the adjacent side:
$\tan(A) = \frac{a}{b}$ $\tan(46.2^\circ) = \frac{30}{b}$