Find the length of the gray arc. Be sure to write the formula, work and answer with units. the arc we know right now is at a 144 degree angle and is 4ft
To find the length of the gray arc, we first need to calculate the circumference of the circle.
The formula to find the circumference of a circle is C = 2πr, where r is the radius of the circle. Since we are given the arc length and the angle, we can calculate the radius using the following formula:
r = (arc length)/(angle in degrees) = 4 ft / (144 degrees) = 1/36 ft/degrees = 0.02778 ft/degree
Now we can find the circumference of the circle:
C = 2π(0.02778 ft/degree) = 0.1745 ft/degree
To find the length of the gray arc, we use the formula:
Arc Length = (angle in degrees/360) * Circumference
Arc Length = (144 degrees / 360) * 0.1745 ft/degree = 0.0698 ft
Therefore, the length of the gray arc is 0.0698 ft.
I mean the apothem is 4ft
Apologies for the confusion.
If the length of the apothem (radius of the circle) is 4 ft, we can use the formula for arc length:
Arc Length = 2πr * (angle in degrees / 360)
Given that the angle is 144 degrees and the radius (apothem) is 4 ft, we have:
Arc Length = 2π(4 ft) * (144 degrees / 360)
Arc Length = 8π ft * 0.4
Arc Length = 3.2π ft
Therefore, the length of the gray arc is approximately 10.053 ft.