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As always, draw a diagram. In triangle XYZ, it should be clear that angle Y = 149°
So, using the law of cosines,
XZ^2 = 6^2 + 7^2 = 2*6*7 cos149°
If we consider X as being at (0,0), then Z is at
(6cos53°+7cos22° , 6sin53°+7sin22°) = ( 10.1, 7.4)
So the bearing of Z from X is 90-θ, where tanθ = 7.4/10.2