Question

find the missing angle. round answer to the nearest degree

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle \(x\) is given by \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(x\) is \(16\) and the hypotenuse is \(20\). So, \(\cos x=\frac{16}{20}\).

Step2: Simplify the ratio

Simplify \(\frac{16}{20}\) to \(\frac{4}{5}=0.8\).

Step3: Find the angle using inverse cosine

We know that \(x = \cos^{-1}(0.8)\). Using a calculator, \(x=\cos^{-1}(0.8)\approx37^{\circ}\).

Answer:

\(37^{\circ}\)