I have solved for most of the parts im just missing the coor

I have solved for most of the parts im just missing the coordinate direction angle Beta of F3.
The magnitude of F3 = 291
The coordinate direction angle alpha of F3=92.9
The coordinate direction angle gamma of F3=53.1


I have tried the answers 44.4, 136, 176, and 103..... None of those were correct. I did have a hint when I calculated 136 that I may have made a rounding error so I\'m assuming 136 is the closest to being right. Please help me solve for the coordinate direction angle beta of F3.

Solution

F1 = -180i lb

F2 = 350cos30(sin40 i + cos40 j) + 350sin30k

F2 = 194.83 i + 232.19j + 175k

so reultant FR = F1 + F2 + F3 = 0


-180i + 194.83 i + 232.19j + 175k + F3 = 0

F3 = - 14.83i - 232.19j - 175k


magnitude of F3 = sqrt(14.83^2 + 232.19^2 + 175^2) = 291.13 lb .....Ans


alpha =180 - cos^-1(14.82/291.13) = 92.92 deg

beta = 180 - cos^-1(232.19/291.13) = 142.88deg

gamma = 180 - cos^-1(175/291.13) = 126.95 deg

I have solved for most of the parts im just missing the coordinate direction angle Beta of F3. The magnitude of F3 = 291 The coordinate direction angle alpha of

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