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: 12

Answer

$b \approx 5$ cm

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 cosine formula to obtain: $\cos{A} = \dfrac{\text{length of adjacent side}}{\text{length of hypotenuse}} \\\cos{72^o}=\dfrac{b}{15}$ Multiply 15 to both sides of the equation to obtain: $\cos{72^o} \cdot 15 = b \\4.635254916= b \\5 \approx b$ Thus, $b \approx 5$ cm.
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