Chapter 7.3, Problem 15E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Find the lengths of the side and the radius of an equilateral triangle whose apothem has the length 8 ft.

To determine

**To find:**

The lengths of the side and the radius of an equilateral triangle.

Explanation

**Approach:**

1) Any radius of a regular polygon bisects the angle at the vertex to which it is drawn.

2) Any apothem of a regular polygon bisects the side of the polygon to which it is drawn.

3) The measure of any central angle of a regular polygon of *n* sides is given by

**Calculation:**

Consider an equilateral triangle *DEF* with *QE* as radius and *QG* as apothem.

It is given that the length of the apothem of the equilateral triangle DEF is 8 ft i.e., *QG* = 8 ft

Use the formula of central angle,

Substitute *n* = 3 in

Therefore,

Any radius of a regular polygon bisects the angle at the vertex to which it is drawn.

Therefore,

Now,

By properties of 30Â°-60Â°-90Â° triangle,

Any apothem of a regular polygon bisects the side of the polygon to which it is drawn

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