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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercises 21 to 30, use the drawings, where provided, to solve each problem, Angle measures should be found to the nearest degree; lengths should be found to the nearest tenth of a unit.

The apothem length of a regular pentagon is approximately 3.44 cm. What is the approximate length of each side of the pentagon?

To determine

To find:

The approximate length of each side of the regular pentagon which has its apothem length as 3.44 cm.

Explanation

Procedure used:

In any right triangle ABC with mA=θ we have the following ratios.

sinθ=OppositeHypotenuse

cosθ=AdjacentHypotenuse

tanθ=OppositeAdjacent

Calculation:

Given:

The length of the apothem of a regular pentagon =3.44 cm.

Let ABCDE be the pentagon with centre ‘o’.

Consider the radii OA and OE of the pentagon adjacent to the apothem OF.

Now, calculate the angle subtended between the radii.

Central angle of the pentagon =360°5

=72°

Thus,

mAOE=72°

The apothem bisects the central angle of the pentagon.

Thus,

mAOF=mEOF=36°

Now, consider the right triangle EOF, in which

OF=3

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