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

Answer 1

1. 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 $\frac{75}{360} * 2\pi  * 100 = 130.8996 = 131 ft$

Answer 2

You have to travel around the sidewalk to get from one path to the other is 131 ft.

We have given that,

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

We have to determine the far would you have to travel around the sidewalk to get from one path to the other.

The gazebo staying in the center of the circular lawn forms a sector with two paths that are 75 degrees from each other.

What is the formula of an arc of a sector?

The formula for the length of an arc of a sector which is the distance between the two paths is Inserting these we have

$\frac{angle}{360}\times 2\pi \times radius$

$radius=\frac{diameter}{2} \\=\frac{200}{2} \\=100ft$

angle=75 degrees

use the above value in the above formula

$=\frac{75}{360}\times 2\pi \times 100\\=131ft$

Therefore, You have to travel around the sidewalk to get from one path to the other is 131 ft.

To learn more about the arc sector visit:

https://brainly.com/question/2293196

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