Magnitude is ?N Direction is ?degree Please show how you got the answer for this

Question

Magnitude is ?N

Direction is ?degree

Please show how you got the answer for this problem. Ive set up 2 equations however webassign still thinks they are wrong and solving them!

96Cos30 - 84cos30 - 46.5cos43 = -17.6

96sin30 + 84sin30 - 46.5sin43 = 52.86

D = Sqrt(-17.6^2 + 52.86^2) = 55.713

WebAssign says this is wrong. The answers they gave said its actually 84.6N & -98.9degreecounter clockwise. Can someone please explain what i am doing wrong and how to come to the right answer?

Thanks!

Three horizontal ropes pull on a large stone stuck in the ground, producing the vector forces and shown in the figure below. Find the magnitude and direction of a fourth force on the stone that will make the vector sum of the four forces zero. The magnitude of Avecbolditalic is 96.0 N, the magnitude of Bvecbolditalic is 84.0 N, and the magnitude of Cvecbolditalic is 46.5 N.

Explanation / Answer

Ax = A*cos(30) = +83.14 N
Ay = A*sin(30) = +48 N

Bx = -B*sin(30) = -42 N

By = B*cos(30) = +72.75 N

Cx = -C*cos(53) = -27.98 N
Cy = -C*sin(53) = -37.14 N

Rx = Ax+Bx+CX = 13.16 N
Ry = Bx+By+Cy = 83.61 N

R = sqrt(Rx^2+Ry^2) = 84.64 N

direction

theta = tan^-1(Ry/Rx) = tan^-1(83.61/13.16) = 81 degrees with +x axis in counter clockwise direction

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