   Chapter 11.4, Problem 35E 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, the area is exactly 18 3  units 2 . Determine the length x. To determine

To find:

The length x for the given triangle whose area is exactly 1813unit2.

Explanation

Formula:

The area of the triangle is given by,

A=12absinγ unit2.

A=12bcsinα unit2.

A=12acsinβ unit2.

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

Calculation:

Given,

Area of the triangle A=183 unit2

From the triangle,

Take a=2x,b=x,andγ=60

By the Law of Sines,

Since, the area of the triangle A=12absinγunit2

A=12(2x)(x)sin(60)

Since, A=183andsin60=3<

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