Question

a right triangle is given. what is the value of the angle theta? 31.6° 35.3° 38.0° 52.0°

Explanation:

Step1: Recall cosine formula

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the adjacent side to $\theta$ is 8 and the hypotenuse is 13, so $\cos\theta=\frac{8}{13}$.

Step2: Find the angle

We know that $\theta = \cos^{- 1}(\frac{8}{13})$. Using a calculator, $\cos^{-1}(\frac{8}{13})\approx52.0^{\circ}$.

Answer:

$52.0^{\circ}$