What is the distance between the following polar coordinates?: # (2,(23pi)/12), (3,(7pi)/8) #

1 Answer
Nov 24, 2016

The distance is # ~~ 4.9897#

Explanation:

Let's begin by rotating both points an additional #pi/12#, because that will make the first point go around a full rotation and its angle will be zero:

#(2, 0), (3, (23pi)/24)#

These points form a triangle with the origin.

side #a = 2#

side #b = 3#

The #angle C" between the sides" = (23pi)/24#

We can use the Law of Cosines to find the length of side c, which is, also, the distance between the two points:

#c = sqrt(a^2 + b^2 - 2(a)(b)cos(C)#

#c = sqrt(2^2 + 3^2 - 2(2)(3)cos((23pi)/24)#

#c ~~ 4.9897#