We have a right triangle and we have to find the measure of A.
We can use trigonometric ratios to relate the measure of A with the known side lengths as:
[tex]\begin{gathered} \sin A=\frac{Opposite}{Hypotenuse}=\frac{10}{16} \\ \sin A=0.625 \\ A=\arcsin(0.625) \\ A\approx38.68\degree \\ A\approx39\degree \end{gathered}[/tex]Answer: A = 39°