In order to find the measure of angle A, we can use the sine relation of this angle.
The sine of a angle in a right triangle is equal the length of the opposite side to the angle over the length of the adjacent leg to the angle.
So we have that:
[tex]\sin (A)=\frac{5}{13}[/tex]
Now, using a calculator to find the inverse function of the sine, we have:
[tex]\begin{gathered} \sin (A)=\frac{5}{13} \\ A=\sin ^{-1}(\frac{5}{13}) \\ A=22.62\degree \end{gathered}[/tex]
So angle A is equal 22.62°.
