Question

A regular pentagon has a perimeter of 60 cm.

What is the measure of central angle CBD?
____°

What is the length of segment CD?
____ cm

Which trigonometric ratio can be used to compare BC to CD using angle CBD?
________

What is the approximate length of BC?
_____ cm

What is the approximate length of BD?
_____cm

Answer 1

A, B, C, C, B

Explanation:

Answer 2

a) ∠CBD is 1/10 the measure of the circle, 36°.

b) CD is 1/10 the perimeter, 6 cm.

c) CD/BC = tan(∠CBD)

d) BC = CD/tan(∠CBD) = (6 cm)/tan(36°) ≈ 8.258 cm

e) BD = (6 cm)/sin(36°) ≈ 10.208 cm