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: 10

Answer

$a \approx 18$ 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 tangent formula to obtain: $\tan{A} = \dfrac{\text{length of opposite side}}{\text{length of adjacent side}} \\\tan{61^o}=\dfrac{a}{b} \\\tan{61^o} = \dfrac{a}{10}$ Multiply 10 to both sides of the equation to obtain: $\tan{61^o} \cdot 10 = a \\18.04047755 = a \\18 \approx a$ Thus, $a \approx 18$ cm.
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