What is the distance between the following polar coordinates?: # (4,(5pi)/3), (3,(7pi)/6) #

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Answer 1 · 2017-12-10T17:54:52

#=> 5#

enter image source here
Here I have drawn an image to show the polar coordinates and there respective lengths

We are trying to find #x#

We see that #alpha = (5pi)/3 - (7pi)/6 = pi/2 #

Now we can use the rule of cosines, but as #alpha # is a right anlge we can just use pythag:

#x^2 = 3^2 + 4^2 #

#=> x = sqrt(9+16)#

#=> x = pm 5 #

Must be postive as lengths can be negative:

#x= 5 =# our length