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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

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

In Review 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?

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 mA=θ we have the following ratios.

sinθ=OppositeHypotenuse

cosθ=AdjacentHypotenuse

tanθ=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

mZCA=α.

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

mZCA=mCAB=α

Thus,

mCAB=α

Here, we have

BC=300 ft = Opposite, and

CA=2200 ft = Hypotenuse

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