   Chapter 11.1, Problem 30E 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.Over a 2000-ft span of highway through a hillside, there is a 100-ft rise in the roadway. What is the measure of the angle formed by the road and the horizontal? To determine

To find:

The angle formed by the road and the horizontal.

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,

Opposite side = 100 ft and hypotenuse = 2000 ft

Let α be the angle formed by the road and the horizontal

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