How do you find the distance between the points with the given polar coordinates #P_1(1.3,-47^circ)# and #P_2(-3.6, -62^circ)#?

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Answer 1 · 2016-11-21T23:13:11

Please see the explanation.

Let's begin by making the radius of #P_2# positive; we do this by adding #180^@# to the angle and changing the sign of the radius:

#P_2 = (3.6, 118^@)#

The angle, #theta# between two line segments drawn from the origin to these two points is:

#theta = 118^@ - -47^@ = 165^@#

Line segment #a = 1.3" units"#
Line segment #b = 3.6" units"#

We can use the Law of Cosines to find the length of line segment c between the two points:

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

#c = sqrt(1.3^2 + 3.6^2 - 2(1.3)(3.6)cos(165^@))#

#c ~~ 4.867" units"#