find the length of arc if an angle measuring 25 degrees is in the circle of radius 6 feet

arc/circumference = 25/360

arc = (2π(6))(25/360) = 5π/6 ft or appr 2.62 ft

12

To find the length of an arc, you need to use the formula:

Arc Length = (Angle / 360) * 2 * π * radius

In this case, the angle is 25 degrees and the radius is 6 feet. π (pi) is a mathematical constant and is approximately equal to 3.14159.

Let's plug in the values into the formula:

Arc Length = (25 / 360) * 2 * 3.14159 * 6

First, we simplify the fraction:

Arc Length = (0.069444) * 2 * 3.14159 * 6

Now, we can calculate the arc length:

Arc Length = 0.138889 * 3.14159 * 6

Arc Length = 0.138889 * 18.84954

Arc Length ≈ 2.61884 feet

Therefore, the length of the arc, when an angle measuring 25 degrees is in a circle with a radius of 6 feet, is approximately 2.61884 feet.