Points #(6 ,7 )# and #(7 ,5 )# are #(2 pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
1 Answer
Feb 17, 2016
Explanation:
Refer to the figure below
Or
Applying Law of Cosines in
#AB^2=r^2+r^2-2r*r*cos 180^@#
#2r^2-2r^2*(-1/2)=(sqrt(5))^2#
#3r^2=5# =>#r=sqrt(5/3)#
Length of the arc
# arc AB=r*alpha# , where alpha is given in radians
#arc AB=sqrt(5/3)*(2*pi)/3*(sqrt(3)/sqrt(3))=2/9*sqrt(15)*pi#
