Question

An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Round your answer to the nearest tenth.

Answer 1

C

Explanation:

Edge2021

Answer 2

Radius r = 3inches
Arc A = 8 inches

We need formula that connects lenght of arc with central angle. That one is fallowing one:

A = 2*r*pi*α/360 where α is central angle. we can see that if α=360, A = 2*r*pi which is exactly the formula for parimeter of circle.

Further more we can express 360 in radians which is 2* pi and get

A = r*α as simpler formula

α = A/r = 8/3 = 2.66666667 ≈ 2.7