MattieSassaman
Answered

A gazebo is located in the center of a large, circular lawn with a diameter f 300ft. Straight paths extend from the gazebo to a sidewalk around the lawn. if two of the paths form a 45degree angle, how far would you have to travel around the sidewalk to get from one path to the other? Round to the nearest foot if necessary. a. 236 ft b. 59ft c. 110ft d. 118ft



Answer :

AL2006
The distance all the way around the sidewalk (the circumference) is 300 pi. 45 degrees is 1/8 of 360 degrees, so the two paths cut 1/8 of the circumference. That's 37.5 pi = 117.81 ft. The nearest whole foot is 118 ft.

The nearest whole foot is 118 ft. Option D is correct.

What exactly is a circle?

It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.

The total distance around the walkway is;300 π ft.

If the angle subtended is 45° then,

45 degrees is 1/8 of 360 degrees, The total circle is divided in the path as;

=45/360

=1/8

The total circumference is divided into the parts as follows;

[tex]\rm \frac{300}{8} =37.5 \pi \\\\ 37.5 \pi=37.5\times 3.14 \\\\ 37.5 \pi =118 \ feet[/tex]

The nearest entire foot is 118 ft.

Hence, option D is correct.

To learn more about the circle, refer to the link:

https://brainly.com/question/11833983.

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