Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 13, Trigonometric Ratios and Functions - 13.1 Use Trigonometry with Right Triangles - 13.1 Exercises - Skill Practice - Page 857: 26


$a \approx 20.38$ $b \approx 17.71$ $B= 41^{\circ}$

Work Step by Step

Here, $\sin A=\dfrac{a}{c}$ This gives: $\sin 49^{\circ}=\dfrac{a}{27} \implies a \approx 20.38$ Now, $\sin B=\dfrac{b}{c}$ This gives: $\sin 41^{\circ}=\dfrac{b}{27} \implies b \approx 17.71$ Since the sum of a triangle is $180^{\circ}$ and the right angle is $90^{\circ}$: $ B=180^{\circ}-49^{\circ}-90^{\circ}=41^{\circ}$
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