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

In a right triangle, $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 80^\circ$, opposite side $= 4$ in, let hypotenuse be $h$. So $\sin(80^\circ)=\frac{4}{h}$.

Step2: Solve for h

Rearrange formula: $h=\frac{4}{\sin(80^\circ)}$. Calculate $\sin(80^\circ)\approx0.9848$. Then $h=\frac{4}{0.9848}\approx4.1$.

Answer:

4.1 in.