Question

A circle has a circumference of 12. It has an arc of 8/5

What is the central angle in the arc?

Answer 1

Answer:48 degrees

Explanation:The central angle of the arc is 48 degrees.

Step-by-step explanation: The question has provided the first clue, which is the circumference of the circle, given as 12 units. Also the length of an arc along the same circumference has been given as 8/5 units. The circumference of a circle is calculated as

Circumference = 2Pi x radius

Also the length of an arc is calculated as

Length of an arc = (X/360) x 2Pi x radius (where ‘X’ is the angle subtended by the arc).

Having known the answer to 2Pi x radius which is 12, and the length of the arc which is 8/5, we can now express the length of an arc as

Length of an arc = (X/360) x 2Pi x radius

8/5 = (X/360) x 12

By cross multiplication we now have

(8 x 360)/ (5 x 12) = X

2880/60 = X

48 = X

Therefore the central angle of the arc is 48 degrees.

Answer 2

14.3 degrees.

Step-by-step explanation:

To find the central angle of an arc, we need to use the formula central angle = arc length / radius * 180/π. In this case, the radius of the circle is 12/2π = 2, so the central angle of the arc is 8/5 / 2 * 180/π = 14.3 degrees.