Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.5 Further Applications of Right Triangles - 2.5 Exercises: 32

Answer

$h = 448.043$ meters

Work Step by Step

Start this problem out by generating two equations for h: $\tan 41.2^{\circ} = \frac{h}{168 + x}$ (1) $h = (168+x)\times \tan 41.2^{\circ}$ $\tan 52.5^{\circ} = \frac{h}{x}$ (2) $h = x \times \tan 52.5^{\circ}$ Set equations (1) & (2) equal to each other and solve for x. $(168+x) \times \tan 41.2^{\circ} = x \times \tan 52.5^ {\circ}$ $(168+x) \times \frac{\tan 41.2^{\circ}}{\tan 52.5^ {\circ}} = x$ $(168+x) \times (0.6717) = x$ $0.328256x = 112.853$ $x = 343.796$ Now plug x into equation (2) to find h. $h = (343.796) \times \tan 52.5^{\circ}$ $h = 448.043$ meters
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