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 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.
183 ft
262 ft
131 ft
3,125 ft

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 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.
183 ft
262 ft
131 ft
3,125 ft

mathstudent55 · Answer

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mathstudent55 · Answer

You need the length of an arc of a circle. The arc has a central angle of 75 deg.
The circumpherence of acircle is c = 2(pi)r
The length of an arc of n degrees is L = (n/360)2(pi)r

anonymous · Answer

that equation isn't working for me

mathstudent55 · Answer

(75/360) x 2 x pi x 100 = (75/360) x 2 x 3.14 x 100 = 130.833