   Chapter 11.3, Problem 45E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 39 to 45, angle measures should be given to the nearest degree; distance should be given to the nearest tenth of a unit.From atop a 200 -ft lookout tower, a fire is spotted due north through an angle of depression of 12 ∘ . Firefighters located 1000 ft due east of the tower must work their way through heavy foliage to the fire. By their compasses, through what angle (measured from the north toward the west) must the firefighters travel? To determine

To calculate:

The angle measured from the north toward the west must the firefighters travel.

Explanation

Given:

From a top 200ft lookout tower, a fire is spotted due to north through an angle of depression of 12 degree. Firefighters located heavy foliage to the fire.

Calculation:

Let h be the height of the tower, d be the distance from the fire to the tower and β be the angle of depression.

tanβ=hdtan12=200dd=200tan12940.92602

Let us assume that d be the distance from firefight to the tower

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