Question

solving for side lengths of right triangles
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.
23.0 in.
22.7 in.
3.9 in.
4.1 in.

Explanation:

Step1: Recall sine - function formula

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Let the opposite side $a = 4$ in and the angle $\theta=80^{\circ}$, and the hypotenuse be $c$. So, $\sin80^{\circ}=\frac{4}{c}$.

Step2: Solve for the hypotenuse $c$

We can re - arrange the formula $\sin80^{\circ}=\frac{4}{c}$ to get $c=\frac{4}{\sin80^{\circ}}$. Since $\sin80^{\circ}\approx0.9848$, then $c=\frac{4}{0.9848}\approx4.1$ in.

Answer:

4.1 in.