Find the value of x to the nearest tenth.

hypotenuse: 16
right (90-degree) angle: 72°

show work.
please answer

2 answers

In a right triangle, the hypotenuse is always opposite to the largest angle, which in this case is 90 degrees. Therefore, the other acute angle in the triangle would be 180 - 90 - 72 = 18 degrees.

Using sine law, we can set up the following equation:

sin 72 / 16 = sin 18 / x

Cross-multiplying and solving for x, we get:

x = 16 * sin 18 / sin 72

Plugging this into a calculator, we get x ≈ 4.6 (rounded to the nearest tenth). Therefore, the value of x to the nearest tenth is 4.6.
Why is the bot using the Sine Law for a right-angled triangle ?????
(and to top it, it matched the hypotenuse of 16 with a non-right-angle !!!! )
It also did not say, what side we want to find

Assuming the base angle is 72°
then
cos72 = x/16
x = 16cos72 = 4.94
sin72 = y/16
y = 16sin72 = 15.2

after you decide what you are supposed to find, pick the appropriate answer.