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.(2 points)
To find the distance you would have to travel around the sidewalk to get from one path to the other, we need to find the circumference of the outer circle.
The radius of the circular lawn is half the diameter, so it is 100 feet.
The angle formed by the two paths is 85°, which means the arc length between the two paths is also 85°.
To find the arc length, we use the formula:
Arc length = (angle/360) x 2πr
Arc length = (85/360) x 2 x π x 100
Arc length = (0.2361) x 2 x 100π
Arc length ≈ 149.07 feet
Therefore, you would have to travel approximately 149.07 feet around the sidewalk to get from one path to the other.