Question

for the right triangle below, find the measure of the angle.
figure is not to scale.
2
8
degrees

Explanation:

Step1: Identify the trigonometric ratio

We know that in a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to the unknown angle is \(2\) and the adjacent side is \(8\). So, \(\tan\theta=\frac{2}{8}=\frac{1}{4}\).

Step2: Find the angle using the inverse tangent function

We use the formula \(\theta = \tan^{- 1}(x)\). Since \(x = \frac{1}{4}\), then \(\theta=\tan^{-1}(\frac{1}{4})\).
Using a calculator, \(\tan^{-1}(\frac{1}{4})\approx14.04^{\circ}\)

Answer:

\(14.04\)