In the following figure, P is the center of the circle, which has a radius of 5 feet. The arc length AB is 10 feet. Find the distance AB Estimate to two decimal places.(Picture Attached) Any help appreciated.
recall that s = rA where s is the arclength, r is the radius and A is the angle of the segment we're concerned with in radians (there's a different formula if you want to work in degrees).
=> A = s/r = 10/5 = 2 radians
now note that ABP forms an isoseles triangle, with base AB. we can find the length of AB using the Law of Cosines
AB^2 = AP^2 + BP^2 - 2AP*BPcosP
=> AB^2 = 5^2 + 5^2 - 2*5*5cos2 ....remember to put your calculator in radian mode
=> AB^2 = 50 - 50(-0.41615) = 70.8
=> AB = 8.41 approximately
I rounded off some when I was calculating so if you want a more "accurate" answer, redo the procedure with more decimal places
if you want to work in degrees, use the formula l = A/360 * 2pi*r where l is the arclength and A is the angle, and then use the Cosine rule for the length of the line once more (this time with your calculator in degrees mode).