   Chapter 11.3, Problem 41E 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

In Exercises 39 to 45, angle measures should be given to the nearest degree; distance should be given to the nearest tenth of a unit.Find the length of the apothem drawn to one of the 6 -in. sides of a regular pentagon.

To determine

To calculate:

The length of the apothem to each of the 6-in. sides of a regular pentagon.

Explanation

Given:

Consider a regular pentagon of side 6 inch.

Definition used:

The trigonometric ratio

Calculation:

Consider a regular pentagon ABCDE and the apothem FG.

The central angle of the regular pentagon is 3605=72.

Thus AFE=72.

Hence the apothem FG bisects the angle and the side AE.

Since AE=6, AG=GE=3.

AFG=GFE=722=36.

Consider the triangle AFG, where AFG=36 and AG=3.

That is α=36 and the length of the opposite leg is 3

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