   Chapter 11.4, Problem 45E 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

Two sides of a triangle have measures a inches and b inches, respectively. In terms of a and b, what is the largest (maximum) possible area for the triangle?

To determine

To Find:

The largest possible area for the triangle, whose two sides have measures a inches and b inches, respectively.

Explanation

1) Calculation:

Given,

Lengths of two sides of a triangle are a inches and b inches,

Let γ be the included angle of the two sides.

By the theorem,

“The area of an acute triangle equals one-half the product of the lengths of two sides and the sine of the included the angle.”

Then, the area of the triangle is A=12absinγ.

In order to find the largest possible area for the triangle, the measure of the angle γ=90

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