Answer
$a \approx 188$ cm
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:
$\tan{A} = \dfrac{\text{length of opposite side}}{\text{length of adjacent side}}
\\\tan{37^o}=\dfrac{a}{b}
\\\tan{37^o} = \dfrac{a}{250}$
Multiply 250 to both sides of the equation to obtain:
$\tan{37^o} \cdot 250 = a
\\188.3885125 = a
\\188 \approx a$
Thus, $a \approx 188$ cm.