instructions: find the measure of the indicated angle to the nearest degree.

Explanation:

Step1: Use sine - function definition

$\sin\theta=\frac{opposite}{hypotenuse}$, here opposite = 42, hypotenuse = 51, so $\sin\theta=\frac{42}{51}$.

Step2: Find the angle

$\theta=\sin^{- 1}(\frac{42}{51})\approx55^{\circ}$

Answer:

$55$