Question

The radius of a regular pentagon measures 7ft. which of the following would be an acceptable equation to use to solve for the measure of the side, s?

(the selected answer is just randomly selected)

Answer 1

Option D.
`cos(54\°)=(0.5s)/(7)`

Explanation:

we know that

A regular pentagon can be divided into 5 isosceles triangles

The length side of the legs of one isosceles triangle is equal to the radius

The vertex angle of one isosceles triangle is equal to 360/5=72 degrees

The base angle of one isosceles triangle is equal to 54 degrees

Let

s------> the length side of the regular pentagon

so

`cos(54\°)=((s/2))/(r)`

substitute the given value

`cos(54\°)=((s/2))/(7)`

`cos(54\°)=(0.5s)/(7)`