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.
o 3.9 in.
o 4.1 in.
o 22.7 in.
o 23.0 in.

Explanation:

Step1: Use sine - function formula

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Given $\theta = 80^{\circ}$ and the opposite side $a = 4$ in. Let the hypotenuse be $c$. So $\sin80^{\circ}=\frac{4}{c}$.

Step2: Solve for $c$

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

Answer:

4.1 in.