How do I find the distance between the points with polar coordinates #(2, 120^circ)# and #(1, 45^circ)#?

1 Answer
Alan P.
Mar 2, 2015

There are polar forms for this but the easiest (for me anyway) is to convert the polar coordinates to Cartesian form then use the Pythagorean theorem.

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Because the angles supplied are standard angles for common right-angles triangles we can easily see that the Cartesian equivalent coordinates are
#( - 1, sqrt(3) )# and #( 1/sqrt(2), 1/sqrt(2) )#

The length of the line is
#sqrt( (-1 - 1/sqrt(2) )^2 + ( sqrt(3) - 1/sqrt(2) ) )#

#= 1.99# (approximately, according to my spreadsheet)

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