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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 11.CR, Problem 24CR
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercises 21 to 30, use the drawings, where provided, to solve each problem, Angle measures should be found to the nearest degree; lengths should be found to the nearest tenth of a unit.

The basket of a hot-air balloon is 300 ft high. The pilot of the balloon observes a stadium 2200 ft away. What is the measure of the angle of depression?Chapter 11.CR, Problem 24CR, In Exercises 21 to 30, use the drawings, where provided, to solve each problem, Angle measures

To determine

To find:

The measure of the angle of depression of a stadium from a hot-air balloon which is 2200 ft away from it and the balloon is 300 ft high.

Explanation

Procedure used:

In any right triangle ABC with m∠A=θ we have the following ratios.

sin⁡θ=OppositeHypotenuse

cos⁡θ=AdjacentHypotenuse

tan⁡θ=OppositeAdjacent

Calculation:

Given:

Height of the balloon =300 ft.

Distance of the balloon from the stadium =2200 ft.

The angle of depression =α.

Let us structure the given figure as follows as a right triangle.

In the above triangle we have

BC=300 ft

CA=2200 ft

m∠ZCA=α.

Since, CZ is parallel to AB and CA is the transversal, by the property that alternate interior angles are equal,

m∠ZCA=m∠CAB=α

Thus,

m∠CAB=α

Here, we have

BC=300 ft = Opposite, and

CA=2200 ft = Hypotenuse

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Sect-11.1 P-1ESect-11.1 P-2ESect-11.1 P-3ESect-11.1 P-4ESect-11.1 P-5ESect-11.1 P-6ESect-11.1 P-7ESect-11.1 P-8ESect-11.1 P-9ESect-11.1 P-10E
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