   Chapter 11.CR, Problem 21CR ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

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

# 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.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

Calculation:

Given:

Height of the tree =12 ft

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)

(i

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