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: Recall sine formula

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

Step2: Substitute values

$\sin80^{\circ}=\frac{4}{h}$, where $h$ is hypotenuse. Then $h = \frac{4}{\sin80^{\circ}}$

Step3: Calculate

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

Answer:

4.1 in.