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the distance z can be found using the law of cosines.
z^2 = 10^2 + 6^2 - 2*10*6*cos137°
or, get the x-y coordinates of A and R (let P be at (0,0)), then use the usual distance formula.
to get the bearing θ of R from A,
tanθ = (Rx-Ax)/(Ry-Ay)