Math

Find the distance between the points with polar coordinates (2, 120°) and (1, 45°)

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  1. there is a formula that says:
    distance between two points (r1,Ø1) and (r2,Ø2) , where both are in polar form is

    √ [ r1^2 + r2^2 - 2(r1)(r2)cos(Ø2-Ø1) }
    = √ [ 4 + 1 - 2(2)(1)cos(120-45) ]
    = √ [ 5 - 4cos75]
    = √[ 5 - (√6 - √2)/4] ----> exact value, or
    = appr. 1.99

    or

    you could convert them to cartesian form

    (2, 120°) = (-1,√3)
    (1,45°) = (√2/2 , √2/2)

    distance = √[ (√2/2 + 1)^2 + (√2/2 - √3)^2 ]
    = 1.99

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  2. notice that the formula I gave is just a variation of the Cosine Law formula.

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