Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 6 - Section 6.2 - Trigonometry of Right Triangles - 6.2 Exercises - Page 489: 61

Answer

tower: 415 ft, window: 152 ft

Work Step by Step

Using the diagram in the book, annotate with $h_{1}$, the part of the tower above the line of eyesight, and with $h_{2}$, the part below the line of eyesight. Upper triangle: $\displaystyle \tan 39^{o}=\frac{h_{1}}{325} \ \Rightarrow \ h_{1}=325\tan 39^{o}$ $h_{1}\approx $263.179810788$\approx$263 ft Lower triangle: $ h_{2}=325\tan 25^{o}\approx$151.5499889$\approx$ 152 ft ( which is also the height of the window) The height of the tower is $h_{1}+h_{2}\approx $263+152=415 ft
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