## Thinking Mathematically (6th Edition)

$a \approx 7$ m
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.