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.
Radius r = 3inches
Arc A = 8 inches
We need formula that connects lenght of arc with central angle. That one is fallowing one:
A = 2rpiα/360 where α is central angle. we can see that if α=360, A = 2rpi 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