Question

for the right triangle below, find the measure of the angle.

Explanation:

Step1: Recall sine - function definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the opposite side to the angle $\theta$ is 9 and the hypotenuse is 17. So, $\sin\theta=\frac{9}{17}$.

Step2: Find the angle using inverse sine

$\theta = \sin^{- 1}(\frac{9}{17})$. Using a calculator, $\theta=\sin^{-1}(\frac{9}{17})\approx31.96^{\circ}\approx32^{\circ}$.

Answer:

$32$