Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.6 Right Triangle Trigonometry - Exercise Set 10.6: 18

Answer

$c \approx 41 \text{ m}$

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: $\sin{A} = \dfrac{\text{length of opposite side}}{\text{length of hypotenuse}} \\\sin{23^o}=\dfrac{16}{c}$ 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: $c = \dfrac{16}{\sin{23^o}} \\c = \dfrac{16}{0.3907311285} \\c = 40.94887464 \\c \approx 41 \text{ m}$
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