   Chapter 11.4, Problem 40E 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

Show that the form of the Law of Cosines written c 2 = a 2 + b 2 − 2 a b  cos  γ reduces to the Pythagorean Theorem when γ = 90 ∘ .

To determine

To Explain:

Law of cosines c2=a2+b22abcosγ reduces to the Pythagorean theorem when γ=90.

Explanation

Given,

Laws of cosines,

c2=a2+b22abcosγ with γ=90

From the statement, the triangle is in the form of right triangle.

Substitute γ=90 in Law of cosines,

c2=a2+b22abcos90

Since, cos 90=0

c2=a2+b22ab(0)

(i

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