A gazebo is located at the center of a large, circular lawn with a diameter of 100 feet. Straight paths extend from the gazebo t

Question

3 years ago

5

A gazebo is located at the center of a large, circular lawn with a diameter of 100 feet. Straight paths extend from the gazebo t

o a sidewalk around the lawn. If two of the paths for a 60 degree angle, how far would you have to travel around the sidewalk to get from one path to the other?
52ft
105ft
26ft
50ft

Mathematics

2 answers:

zzz [600] · Answer 1 · 2022-07-20T05:20:54+03:00

Answer: The first option, 52 ft.

Step-by-step explanation:

The data we have is:

The diameter of the lawn is 100ft.

Between the two pats, we have a 60° angle, so we want to calculate the distance between both paths, walking around the circle, this would be the length of the arc of 60°.

Now, first, we know that the perimeter of the circle is equal to 2*pi*radius.

So a section of the perimeter can be calculated as:

L = Angle*radius.

But we need to write the angle in radians.

We know that 180° = pi = 3.14

then (60°/180°)*3.14 = 1.04

60° is equivalent to 1.04 radians.

Now, we have the diameter of our circle, and we know that the radius is equal to half the diameter, so if d = 100ft, r = 100ft/2 = 50ft.

Then the length of the arc is:

L = 1.04*50ft = 52.3 ft

Then the correct answer is the first one (where the result is rounded to the next whole number, 52 ft.)