Question

for the right triangle below, find the measure of the angle. please show your answer to one decimal place.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to the angle (let the angle be \(\theta\)) is \(9\) and the hypotenuse is \(13\). So, \(\cos\theta = \frac{9}{13}\).

Step2: Find the angle using inverse cosine

\(\theta=\cos^{- 1}(\frac{9}{13})\). Using a calculator, \(\cos^{-1}(\frac{9}{13})\approx46.5674^{\circ}\). Rounding to one decimal place.

Answer:

\(46.6^{\circ}\)