M<A = 39, AC = 11 Find the LENGTH. what is the length?

enter image source here

1 Answer
Feb 17, 2018

11π3

Explanation:

The angle CAB sweeps out some fraction of A's full 360, and subsequently the same fractional part of A's circumference. To find what the fraction is, we can divide CAB by 360:

mCAB360=55360=1172

So, CAB sweeps out 1172 of the circle's circumference.

The circumference of any circle is equal to the product of π and the diameter d of the circle, which is itself equal to twice the radius, 2r. Here, we're given r=AC=12, so the circle's circumference is π2(12)=24π.

So, the length of the arc BC=117224π=24π1172

24 and 72 both have the factor 24 in common, so we can reduce down to

11π3

And we're done.