Question

A gazebo is located in the center of a large circular lawn with a diameter of 200 feet. Straight paths extend from the gazebo to a sidewalk around the lawn. If two of the paths form an 85° angle, how far would you have to travel around the sidewalk to get from one path to the other? Show all necessary work and calculations to receive full credit.

Answer 1

To find the distance around the sidewalk to get from one path to the other, we need to find the circumference of the circle with a diameter of 200 feet.

First, we find the radius of the circle by dividing the diameter by 2:
Radius = 200 ft / 2 = 100 ft

Next, we calculate the circumference of the circle using the formula:
Circumference = 2 * π * radius

Circumference = 2 * π * 100 ft ≈ 628.32 ft

The angle between the two paths is 85°, which means that the distance around the circle between the two paths is 85/360 of the total circumference.

Distance between paths = (85/360) * Circumference
Distance between paths = (85/360) * 628.32 ft
Distance between paths ≈ 148.05 ft

Therefore, you would have to travel approximately 148.05 feet around the sidewalk to get from one path to the other.