Question

A circle with radius 142.5 has an arc with a 24 degree angle. What is the length of the arc?

Answer 1

59.69 units

Step-by-step explanation:

TOTAL circumference of this circle = pi * d = pi * 2r = 895.354

now you want 24 degrees of the entire 360 degrees

24/ 360 * 895.354 = 59.69 units

Answer 2

Answer: 59.690260418206

The result is approximate. Round that value however you need to.

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Step-by-step explanation:

For a circle with radius r = 142.5, the full distance around the edge (aka perimeter aka circumference) is found by using the formula below.

C = 2*pi*r

C = 2*pi*142.5

C = 895.353906273091

That value is approximate. I used my calculator's stored value of pi to get the most accuracy possible.

That value of roughly 895 represents the distance around a full circle of that radius, but we only want a 24 degree pizza slice.

In other words, we want 24/360 = 1/15 of the full perimeter

(1/15)*895.353906273091 = 59.690260418206