Question

find the measure of the indicated angle. round your answer to the nearest tenth. answer: 19.4

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to the angle \(\theta\) is \(8\) and the adjacent side is \(20\). So, \(\tan\theta=\frac{8}{20}\).

Step2: Calculate the angle

We know that \(\theta = \tan^{- 1}(\frac{8}{20})\).
First, simplify \(\frac{8}{20}=\frac{2}{5} = 0.4\).
Then, \(\theta=\tan^{-1}(0.4)\).
Using a calculator, \(\tan^{-1}(0.4)\approx21.8^{\circ}\)

Answer:

\(21.8^{\circ}\)