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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.
a. 183 ft
b. 262 ft
c. 131 ft
d. 3,125 ft​

Respuesta :

Answer: The answer is 131 ft.

Step-by-step explanation:

The gazebo staying in the centre of the circular lawn forms an sector with the two paths that are 75 degrees to each other. The formula for length of an arc of a sector which is the distance between the two paths is \frac{angle}{360} * 2\pi * radius\\radius = \frac{diameter}{2} = \frac{200}{2} = 100 ft\\ angle = 75 degrees.\\

Inserting these we have \frac{75}{360} * 2\pi * 100 = 130.8996 = 131 ft.

Hope it helps you !!

~Adrianna

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