   Chapter 11.1, Problem 24E 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 21 to 26, find the measures of the angles named to the nearest degree. To determine

To measure:

The angle named to the nearest degree.

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.

Formula used:

sinθ=oppositehypotenuse

Given:

By using Pythagoras theorem, that is

c2=a2+b2

Let b be the adjacent side of the triangle.

From, the diagram we have c=10 and a=3

122=52+b2144=9+b2b2=14425b2=119b=119b=10.9

For angle α, the opposite side is 5 inches and hypotenuse side is 12 inches.

Then,

sin α=oppositehypotenusesin α=512sin α=0

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