## Trigonometry (10th Edition)

Published by Pearson

# 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

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.