## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 7 - Test - Page 354: 17

#### Answer

The height of the leaning tree is 13.7 meters

#### Work Step by Step

Let A be the point at the bottom of the tree. Let B be the point on the ground where the angle of elevation is $66^{\circ}$. Let C be the point at the top of the tree. The points ABC form a triangle. We can find the angle at point A: $A = 90^{\circ}-8.0^{\circ} = 82^{\circ}$ The angle at point B is $66^{\circ}$ We can find the angle at point C: $C = 180^{\circ}-82^{\circ} -66^{\circ} = 32^{\circ}$ We can use the law of sines to find the length between the bottom and top of the tree: $\frac{AC}{sin~B} = \frac{AB}{sin~C}$ $AC = \frac{AB~sin~B}{sin~C}$ $AC = \frac{(8.0~m)~sin~66^{\circ}}{sin~32^{\circ}}$ $AC = 13.8~m$ We can find the height $h$ of the leaning tree: $\frac{h}{AC} = cos(8.0^{\circ})$ $h = (AC)~cos(8.0^{\circ})$ $h = (13.8~m)~cos(8.0^{\circ})$ $h = 13.7~m$ The height of the leaning tree is 13.7 meters

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