Question

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

Explanation:

Step1: Identify the trigonometric ratio

We want to find angle \(B\). Given the adjacent side \(BC = 4\) and the hypotenuse \(AB=5\) for angle \(B\), we use the cosine - ratio \(\cos B=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos B=\frac{4}{5}\).

Step2: Find the angle

We know that \(B = \cos^{-1}(\frac{4}{5})\). Using a calculator, \(B=\cos^{-1}(0.8)\approx36.9^{\circ}\).

Answer:

\(36.9\)