   Chapter 11.2, Problem 43E 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 Exercise 42 and 43, use the drawing and the formula from Exercise 41.Find the area of an isosceles triangle for which s = 4.8   inches and the measure of the base angle is 72 ∘ .

To determine

To find:

The area of an isosceles triangle for which s=4.8inches and the measure of the base angle is 72 by using the given figure,

Explanation

Consider the following figure,

The area of the triangle is given below,

A=s2sinθcosθ

We know that in any triangle the sum of the angle is equal to 180.

That is

vertex angle + 2 ( base angle ) = 180

vertex angle + 2 ( 72)= 180

vertexangle=180+144vertexangle=36

Given that s=4.8inches and the measure of the vertex angle is 36.

From the above figure shows that the measure of the vertex angle is

2θ=36θ=362θ=18

Substitute the values in the area formula to get the following,

A=(4

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