Question

He equation sin (40 degree) equals StartFraction b Over 20 EndFraction can be used to determine the length of line segment AC.

Triangle A B C is shown. Angle A C B is a right angle. The length of side A C is b and the length of hypotenuse A B is 20 centimeters.

What is the length of ? Round to the nearest tenth.

Answer 1

The correct answer is 12.9

Explanation:

I took the test on edge

Answer 2

The value of b is 12.9 cm

The value of a is 15.3 cm

Explanation:

see the attached figure to better understand the problem

Find the value of b

we know that

in the right triangle ABC

The function sine of angle of 40 degrees is equal to divide the opposite side to the angle of 40 degrees (AC) by the hypotenuse (AB)

so

`sin(40\°)=AC/AB`

Solve for AC

`AC=(AB)sin(40\°)`

substitute the given value

`AC=(20)sin(40\°)`

`AC=12.9\ cm`

therefore

The value of b is 12.9 cm

Find the value of a

we know that

in the right triangle ABC

The function cosine of angle of 40 degrees is equal to divide the adjacent side to the angle of 40 degrees (BC) by the hypotenuse (AB)

so

`cos(40\°)=BC/AB`

Solve for BC

`BC=(AB)cos(40\°)`

substitute the given value

`BC=(20)cos(40\°)`

`BC=15.3\ cm`

therefore

The value of a is 15.3 cm