Question

consider the following triangle. determine the measure of the angle represented by θ using the inverse - tangent function. a. 50.2° b. 56.4° c. 39.8° d. 33.6°

Explanation:

Step1: Recall tangent - ratio formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side to angle $\theta$ is $5$ m and the adjacent side is $6$ m. So, $\tan\theta=\frac{5}{6}$.

Step2: Use inverse tangent function

To find $\theta$, we use $\theta = \tan^{- 1}(\frac{5}{6})$. Using a calculator, $\theta=\tan^{-1}(\frac{5}{6})\approx39.8^{\circ}$.

Answer:

C. $39.8^{\circ}$