Answer
$A \approx 23^o$
Work Step by Step
RECALL:
In a right triangle,
$\sin{A} = \dfrac{\text{length of opposite side}}{\text{length of hypotenuse}}
\\\cos{A} = \dfrac{\text{length of adjacent side}}{\text{length of hypotenuse}}
\\\tan{A} = \dfrac{\text{length of opposite side}}{\text{length of adjacent side}}$
Use the tangent formula to obtain:
$\tan{A} = \dfrac{\text{length of opposite side}}{\text{length of adjacent side}}
\\\tan{A}=\dfrac{10}{24}
\\\tan{A} = 0.41\overline{6}$
Use the inverse tangent function of a scientific calculator to obtain:
$A = \tan^{-1}{0.6}
\\A = 22.61986495^o
\\A \approx 23^o$