What is the distance between the following polar coordinates?: # (8,(7pi)/4), (5,(15pi)/8) #

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Answer 1 · 2016-11-01T16:29:15

The distance is #~~ 3.88#

The origin and these two points:

#(8, (7pi)/7) and (5, (15pi)/8)#

Form a triangle with,

side #a = 8#,
side #b = 5#,

and the angle between them is,

#C = (15pi)/8 - (7pi)/4 = pi/8#.

The distance between the two points is the length of side c, in the equation for the Law of Cosines:

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

#c^2 = 8^2 + 5^2 - 2(8)(5)cos(pi/8)#

#c ~~ 3.88#