Thinking Mathematically (6th Edition)

$c \approx 41 \text{ m}$
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: $\sin{A} = \dfrac{\text{length of opposite side}}{\text{length of hypotenuse}} \\\sin{23^o}=\dfrac{16}{c}$ Multiply $c$ to both sides of the equation to obtain: $c \cdot \sin{23^o} = 16$ Divide $\sin{23^o}$ on both sides of the equation to obtain: $c = \dfrac{16}{\sin{23^o}} \\c = \dfrac{16}{0.3907311285} \\c = 40.94887464 \\c \approx 41 \text{ m}$