Points #(8 ,5 )# and #(7 ,6 )# are #( pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
1 Answer
Nov 19, 2016
Explanation:
The length of the chord is:
Two radii, each drawn from the center to its respective end of the chord, form a triangle with the chord, therefore, we can use a variant of the Law of Cosines where
Substitute
NOTE: At this point, we should realize that an isosceles triangle with the third angle equal to
The arc length is,