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 degree angle, how far would you have to travel around the sidewalk to get from one path to another?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the distance around the sidewalk from one path to another, 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 C is the circumference and d is the diameter.

C = π(200 feet)
C ≈ 628.32 feet

Now that we have the circumference of the circle, we need to determine what fraction of the circle is between the two paths forming a 75 degree angle. Since the angle between the two paths is 75 degrees, the fraction of the circle between the paths is 75/360 = 0.2083.

To find the distance around the sidewalk between the two paths, we multiply the circumference by the fraction of the circle between the paths.

628.32 feet * 0.2083 ≈ 130.94 feet

Therefore, to get from one path to another, you would have to travel approximately 130.94 feet around the sidewalk.