Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Acute Angles and Right Triangles - Section 2.4 Solving Right Triangles - 2.4 Exercises: 22

Answer

$\angle A = 44^{\circ}$ $b\approx 21.4m$ $a\approx 20.6m$

Work Step by Step

1. Given $\angle B = 46^{\circ}$; $c = 29.7ft$ 2. Find side $a$ by using sine $\sin B = \frac{b}{c}$ => $b = c\times\sin B = 29.7 \times\sin 46^{\circ}\approx 21.4 m $ 3. Find side $b$ by using cosine $\cos B = \frac{a}{c}$ => $a = c\times\cos B= 29.7 \times\cos 46^{\circ} \approx 20.6 m$ 4. Angles in a triangle should add up to 180 degrees $\angle A = 180^{\circ} -90^{\circ} -46^{\circ} =44^{\circ}$
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