Question

find the measure of the indicated angle (?) round to the nearest tenth.

Explanation:

Step1: Recall tangent function

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side to the indicated angle is 34 and the adjacent side is 39. So, $\tan\theta=\frac{34}{39}$.

Step2: Find the angle

We need to find $\theta$. Using the inverse - tangent function, $\theta = \tan^{- 1}(\frac{34}{39})$.
Calculating $\tan^{-1}(\frac{34}{39})\approx40.9^{\circ}$. Rounding to the nearest tenth, $\theta\approx41^{\circ}$.

Answer:

$41^{\circ}$