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: 15

Answer

$c = 20.5 ft$ $\angle A= 37.7 ^{\circ}$ $\angle B =52.3 ^{\circ}$

Work Step by Step

1. $a = 12.5 ft$; $b = 16.2 ft$ $\angle C = 90^{\circ}$ 2. $\tan A = \frac{a}{b}= \frac{12.5}{16.2}$ $\angle A = \tan^{-1} (0.771604383) \approx 37.7^{\circ}$ 3. $\angle A+ \angle B = 90^{\circ}$ $ \angle B = 90^{\circ} -37.7^{\circ} = 52.3^{\circ}$ 4. Pythagoream theorem $c^2 = 12.5^2 + 16.2^2$ $c = \sqrt {156.25+262.44}$ $c = 20.5 ft$ consider only positive root, as length always positive in trigonometry
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