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.)
