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This is a standard relative motion type of question. You are given complete information on the velocity vectors for A and P (both x- and y-components). And, you are asked to find the velocity of P with respect to A.
To do so, use the basic equation for relative velocity between two points: vP/A = vP - vA. From this result, you are then asked to find the angle of the observed velocity of P, with this last step being just trig.