What is the distance between $(2 , (5 pi)/4 )$ and $(8 , (2 pi )/3 )$ ?

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Answer 1 · 2016-10-05T16:23:52

The distance between them is $~~ 8.73$

Because the origin and the two given points form a triangle, one can use the Law of Cosines for this type of problem:

$c² = a² + b² - 2(a)(b)cos(C)$

where $a = 2, b = 8,$ and $C = 5pi/4 - 2pi/3 = 7pi/12$ :

$c² = 2² + 8² - 2(2)(8)cos(7pi/12)$

$c ~~ 8.73$

What is the distance between (2 , (5 pi)/4 )(2 , (5 pi)/4 ) and (8 , (2 pi )/3 )(8 , (2 pi )/3 )?