   Chapter 11.CT, Problem 17CT ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# On the basis of the drawing provided, complete this form Of the Law of Cosines. a 2 = _________ To determine

To complete:

The law of cosine using the drawing given.

Explanation

Given:

The Law of cosines.

Theorem:

In any acute triangle ABC,

c2=a2+b2-2ab cos γ

b2=a2+c2-2ac cos β

a2=b2+c2-2bc cos α, which is called the Law of Cosines.

Calculation:

In the below diagram, BC=a, CA=b, and AB=c.

In right triangle BDC, m2+n2=a2

m2=a2-n2

In right triangle ABD, b-m2+n2=c2

b2-2bm+m2+n2=c2

Substituting m2=a2-

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