Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 5.4, Problem 20E

(a)

To determine

To find: The radius of the circumscribed circle.

(a)

Expert Solution

Answer to Problem 20E

Radius = 13.3

Explanation of Solution

Given information: Geometry: the apothem of a regular pentagon is 10.8 centimeters.

Calculation:

Given the apothems 10.8, find the radius of the circumscribed circle. This is the same as the radius of the regular pentagon.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.4, Problem 20E , additional homework tip 1

This is the triangle we need to find the hypotenuse and we know the adjacent side. This is a cosine problem.

cos36∘=10.8rr=10.8cos36∘r=13.3

(b)

To determine

To find: the length of a side of the pentagon.

(b)

Expert Solution

Answer to Problem 20E

Side of pentagon = 15.6

Explanation of Solution

Given information: Geometry: the apothem of a regular pentagon is 10.8 centimeters.

Calculation:

Given the apothems 10.8, find the radius of the circumscribed circle. This is the same as the radius of the regular pentagon.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.4, Problem 20E , additional homework tip 2

This is the triangle we need to find the opposite side (which is ½ of the pentagon’s side that we are trying to find) and we know the adjacent side. This is a tangent problem.

tan36∘=x10.8x=10.8×tan36∘x=7.8

Now this is only half the side, so we need to double it.

Thus, the side of the pentagon = 15.6.

(c)

To determine

To find: The perimeter of the pentagon.

(c)

Expert Solution

Answer to Problem 20E

Perimeter of pentagon = 78

Explanation of Solution

Given information: Geometry: the apothem of a regular pentagon is 10.8 centimeters.

Calculation:

We found the side of the pentagon to be 15.6 in the last problem.

A pentagon has 5 sides,

So the perimeter = 5×15.6=78

Chapter 5.4, Problem 19E

Chapter 5.4, Problem 21E

Chapter 5 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 5.1 - Prob. 1CFU Ch. 5.1 - Prob. 2CFU Ch. 5.1 - Prob. 3CFU Ch. 5.1 - Prob. 4CFU Ch. 5.1 - Prob. 5CFU Ch. 5.1 - Prob. 6CFU Ch. 5.1 - Prob. 7CFU Ch. 5.1 - Prob. 8CFU Ch. 5.1 - Prob. 9CFU Ch. 5.1 - Prob. 10CFU

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