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

Answer 1

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.

Answer 2

I mean the apothem is 4ft

Answer 3

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.