A woman walks 143m in the direction 55° east of north, then 178m directly east. Find the magnitude of the displacement vector. Answer: 306m Relevant equations: I will use vA as a shorthand to represent vector A and ||vA|| to represent the magnitude. Ax = ||vA||cos(theta) Ay = ||vA||sin(theta) ||vA|| = sqrt(Ax^2 + Ay^2) -------------------------------- Since I know the magnitude of vA (assuming vA is the starting vector) and the angle in which she left the origin of the coordinate grid I can use the two equations stated above to find the values of Ax and Ay. Ax = 143m*cos(55) = 82.02m Ay = 143m*sin(55) = 117.14m Now I add vA + vB (<82.02m, 117.14m> + <178m, 0m>) to obtain vC, the vector displacement between her starting position to her final position. However, when I go and find the magnitude of the vector I always come out with the wrong answer, 285.19m. vC = <260.02m, 117.14m> ||vC|| = sqrt(260.02m^2 + 117.14m^2) = sqrt(81332.18m^2) = 285.19m. What did I do wrong? I thought this would be a simple problem but I keep coming out with the wrong answer. Can someone help me?