Question

find the measure of the angle. round to the nearest tenth.

Explanation:

Step1: Identify trigonometric ratio

In right - triangle $ABC$, we know the adjacent side $BC = 4$ to angle $\theta$ and the hypotenuse $AB = 5$. We use the cosine function $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos\theta=\frac{4}{5}=0.8$.

Step2: Find the angle

We use the inverse - cosine function $\theta=\cos^{- 1}(0.8)$. Using a calculator, $\theta=\cos^{-1}(0.8)\approx36.9^{\circ}$.

Answer:

$36.9$