Question

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

Explanation:

Step1: Recall tangent - inverse formula

In a right - triangle, if the opposite side to the angle $\theta$ is $a$ and the adjacent side is $b$, then $\tan\theta=\frac{a}{b}$, and $\theta = \tan^{- 1}(\frac{a}{b})$. Here, the opposite side $a = 34$ and the adjacent side $b = 39$.

Step2: Calculate the angle

$\theta=\tan^{-1}(\frac{34}{39})\approx\tan^{-1}(0.8718)$. Using a calculator in degree mode, $\theta\approx41.1^{\circ}$. Rounding to the nearest tenth, $\theta\approx41.1^{\circ}$.

Answer:

$41.1^{\circ}$