a right triangle has one side that measures 4 in. the angle opposite that side measures 80°. what is the…

Answer:

B. 4.1 in.

Explanation:

Step1: Recall sine - rule in right - triangle

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

Step2: Solve for the hypotenuse $c$

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