52.1º
1) As we have a right triangle, then we can make use of a trigonometric ratio sine and the arcsine:
[tex]\begin{gathered} \sin (\theta)=\frac{opposite\text{ leg}}{\text{hypotenuse}} \\ \sin (\theta)=\frac{15}{19} \\ \end{gathered}[/tex]2) Let's calculate the arcsine of 15/19 to get the angle measure:
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{15}{19}) \\ \theta\text{ =52.1363}\approx52.1 \end{gathered}[/tex]3) As the measure of the angle is given either in radians or degrees, then the answer is 52.1º
