Question

find the measure of the indicated angle. * 1 point 23 14 31° 37° 59° 53°

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the adjacent side to the unknown angle is $14$ and the hypotenuse is $23$. So, $\cos\theta = \frac{14}{23}$.

Step2: Calculate the angle

We know that $\theta=\cos^{- 1}(\frac{14}{23})$. Using a calculator, $\cos^{-1}(\frac{14}{23})\approx52.99^{\circ}\approx53^{\circ}$

Answer:

$53^{\circ}$