Question

PLEASE HELP

A regular pentagon has been inscribed in a circle of radius 16 cm, as shown in the diagram below. Segment NM is an altitude of ANB. Find the following:
m ANM=
Length of segment AM=
The perimeter of regular polygon ABCDE=

Answer 1

m < ANM = 36 degrees.

AM = 9.40 cm to the nearest hundredth.

Perimeter = 94.05 cm to the nearest hundredth.

Explanation:

As we have a regular pentagon:

m < ANB = 360 / 5

= 72 degrees

So m < ANM = 1/2 * 72

= 36 degrees.

In the triangle ANM, AN = 16 so

sin 36 = Am / 16

AM = 16 sin36

= 9.4045 cm.

AB = 2 * AM = 18.809 cm

So as all sides are equal:

Perimeter = 5 * 18.809

= 94.05 cm.