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: 25


$b \approx 55.98$ and $c \approx 57.96$ $ A=15^{\circ}$

Work Step by Step

Here, $\tan B=\dfrac{b}{a}$ This gives: $\tan 75^{\circ}=\dfrac{b}{15} \implies b \approx 55.98$ Now, $\sin A=\dfrac{a}{c}$ This gives: $\sin 75^{\circ}=\dfrac{15}{c} \implies c \approx 57.96$ Since the sum of a triangle is $180^{\circ}$ and the right angle is $90^{\circ}$: $ A=180^{\circ}-75^{\circ}-90^{\circ}=15^{\circ}$
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