Answer
$a \approx 7$ m
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 to obtain:
$\sin{A} = \dfrac{\text{length of opposite side}}{\text{length of hypotenuse}}
\\\sin{34^o}=\dfrac{a}{13}$
Multiply 13 to both sides of the equation to obtain:
$\sin{34^o} \cdot 13 = a
\\7.269507745= a
\\7 \approx a$
Thus, $a \approx 7$ m.