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? Ro und your answer to the nearest tenth.
1 answer:
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
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