Question

please help!
Find the measure of a central angle that intercepts an arc of 3 inches in a circle whose radius is 8 inches.



0.375 rad

1.05 rad

2.3 rad

Answer 1

This is an incredibly elementary explanation, but it demonstrates the point.

Think of taking the radius out and laying it on the edge of the circle. This represents 1 rad, but it is actually 8 inches. Divide it into 8 segments, each 1 inch long. Remove 5 so you're left with 3 inches. This is 3/8 of the original. 3/8 * 1 rad = 3/8 rad, or 0.375 rad. That's the arc measure.

Now, remember that central angles, unlike inscribed angles, take the exact same measure as their arc. Inscribed angles are half the measure. The angle measure is 0.375 rad.