Question

a regular pentagon has an apothem of 7.43 cm. Find the length of a side of the pentagon and the length of the radius of the circumscribed circle

Answer 1

Since it is a pentagon, what are the measures of the acute angles in the right triangle formed by the apothem and the radius?

Answer 2

it doesn't give me that:/

Answer 3

No. You have to figure it out. First, the sum of the angles in a polygon = n-2(180) where n is the number of sides. For a pentagon, this is 5-2(180)=540. then divide by 5 for each of 5 large angles in the pentagon, and then divide by 2 for the angle formed by the radius in the right angle. This is 540/5=108 divided by 2 = 54 degrees in the right angle. Now that you know the angle , then use trig to solve the problem...

Answer 4

oh! Thank you!!:D

Answer 5

You are welcome!