Answer
$a \approx 182$ 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 cosine formula to obtain:
$\cos{A} = \dfrac{\text{length of adjacent side}}{\text{length of hypotenuse}}
\\\cos{34^o}=\dfrac{b}{220}$
Multiply 220 to both sides of the equation to obtain:
$\cos{34^o} \cdot 220 = b
\\182.388266 = b
\\182 \approx a$
Thus, $a \approx 182$ in.