Question

a right triangle has one side that measures 4 in. the angle opposite that side measures 80°. what is the length of the hypotenuse of the triangle? round to the nearest tenth. 3.9 in. 4.1 in. 22.7 in. 23.0 in.

Explanation:

Step1: Apply sine formula

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Rearrange to solve hypotenuse

$\text{hypotenuse}=\frac{\text{opposite}}{\sin\theta}$

Step3: Substitute values

$\text{hypotenuse}=\frac{4}{\sin80^\circ}\approx\frac{4}{0.9848}\approx4.1$

Answer:

B. 4.1 in.