   Chapter 11.1, Problem 32E 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.A 12-ft rope secures a rowboat to a pier that is 4ft above the water. Assume that the lower end of the rope is at “water level”. What is the angle formed by the rope and the water? Assume that the rope is taut. To determine

To find:

The angle formed by the water and the rope.

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 = 4 ft and hypotenuse = 15 ft

Let α be the angle formed by the water and the rope.

We know that,

sinθ=oppositeHyp

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