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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.

In the evening, a tree that stands 12 ft tall casts a shadow. If the angle of depression from the top of the tree to the tip of the shadow is 55 ° , what is the length of the shadow?

To determine

To find:

what is the length of the shadow.

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 tree =12 ft

Length of the shadow =x

Angle of depression of the shadow =55°

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

In the above figure CZ is parallel to AB and CA is the transversal.

Thus, by the property that the alternate interior angles are equal, we have

mZCA=mCAB=55°

Thus, in ABC

mA=55°

BC=12 ft (Height of the tree)

AB=x (Length of the shadow)

(i

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