Answer
$a \approx 37\text{ in} $
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 sine formula above to obtain:
$\sin{48^o} = \dfrac{a}{50}$
Multiply 50 on both sides of the equation to obtain:
$50 \cdot \sin{48^o} = a$
Use a scientific calculator to obtain:
$50 \cdot 0.7431448255 = a
\\37.15724127 = a
\\a \approx 37\text{ in} $
