A gazebo is located in the center of a large, circular lawn with a diameter of 200 feet. Straight paths extend from the

Question

gazebo to a sidewalk around the lawn. If two of the paths form a 75° angle, how far would you have to travel around the
sidewalk to get from one path to the other? Round your answer to the nearest foot if necessary.

(1 point)

183 ft

262 ft

131 ft

3,125 ft

Answer 1

131 ft

To find the distance to travel 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. The formula for the circumference of a circle is C = πd, where d is the diameter.

C = π(200) = 200π ft

Since the two paths form a 75° angle, the distance traveled along the curve of the circle would be 1/4 of the total circumference (as 75° is 1/4 of 360°).

1/4 * 200π ≈ 50π ≈ 156.86 ft

Rounding to the nearest foot, we get 131 ft.