   Chapter 11.4, Problem 36E 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

For the triangle shown, use the Law of Cosines to determine b. To determine

To find:

The length b of the given triangle by using the law of cosines.

Explanation

Formula:

The Law of Cosines

a2=b2+c22bccosα

b2=a2+c22accosβ

c2=a2+b22abcosγ

Where α, β, and γ is the acute angle of the triangle, and a, b, and c is the sides of the triangle.

Calculation:

Given,

From the triangle,

Take a=2,c=23,andγ=60

By the law of cosines,

c2=a2+b22abcosγ

(23)2=(2)2+b22(2)bcos(60)

Since, cos60=12

4(3)=4+b2

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