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: 17

Answer

$c = 40$ 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: $\sin{A} = \dfrac{\text{length of opposite side}}{\text{length of hypotenuse}} \\\sin{30^o}=\dfrac{20}{c}$ Multiply $c$ to both sides of the equation to obtain: $c \cdot \sin{30^o} = 20$ Divide $\sin{30^o}$ on both sides of the equation to obtain: $c = \dfrac{20}{\sin{30^o}} \\c = \dfrac{20}{0.5} \\c = 40 \text{ m}$
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