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

We know that \(\theta = \cos^{-1}(\frac{9}{13})\). Using a calculator, \(\cos^{-1}(\frac{9}{13})\approx46.2^{\circ}\) (rounded to one decimal place).

Answer:

\(46.2^{\circ}\)