   Chapter 11.1, Problem 31E 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 27 to 34, use the drawings, where provided, to solve each problem. Angle measures should be given to the nearest degree; distances should be given to the nearest tenth of a unit.From a cliff, Phillip observes an automobile through an angle of depression of 23◦. If the cliff is 50ft high, how far is the automobile from Phillip? To determine

To find:

The distance between the automobile and Phillip.

Explanation

In a right angle triangle,

1) The side PQ, which is opposite to the right angle PRQ is called the hypotenuse.

(The hypotenuse is the longest side of the right triangle.)

2) The side RQ is called the adjacent side of angle θ.

3) The side PR is called the opposite side of angle θ.

Hence, the sine ratio for an acute angle is oppositehypotenuse

Given:

From, the given diagram,

Angle of depression is 23, opposite side = 50 ft(Cliff height).

Let a be the hypotenuse, that is the distance between automobile and Phillip.

We know that,

sinθ=oppositeHypotenuse

sin23°=50a

From the table 11

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