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

Answer 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

Answer 2

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