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 - function formula

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

Step2: Solve for the hypotenuse $c$

We can rewrite the equation as $c=\frac{4}{\sin80^{\circ}}$. Since $\sin80^{\circ}\approx0.9848$, then $c=\frac{4}{0.9848}\approx4.1$.

Answer:

B. 4.1 in.