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 - Page 83: 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
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.