Given Magnitude of P and Q and the Magnitude of the sum of P and Q. How would yo

Question

Given Magnitude of P and Q and the Magnitude of the sum of P and Q. How would you find the angles between P and the sum, and Q and the Sum. Use P = 100N, Q = 200N, and the sum of P&Q = 250 N. PLEASE SHOW WORK

Explanation / Answer

(P+Q)^2 = P^2 + Q^2 + 2PQcos(P,Q) where cos(P,Q) denotes cosine of the angle between P and Q =>250^2 = 100^2 + 200^2 + 2*100*200*cos(P,Q) =>Cos(P,Q) = 0.3125 =>(P,Q) = 71.79 degrees. Let Angle between P and P+Q = theta Then Tan(Theta) = Qsin(P,Q)/(P+Qcos(P,Q)) = 1.16913 => Theta = Angle between P and P+Q = 49.49 Degrees And angle between Q and P+Q = (P,Q)-Angle between P and P+Q = 71.79-49.49 = 22.3 Degrees

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