Determine the direction angle beta of the force F acting on

Determine the direction angle beta of the force F acting on the stake. Enter the answer in units of degrees Given F_h = 40 N theta = 70 deg c = 3 d = 4

Solution

end points of Fh = (40 cos70, 40 sin70, 0) = (13.68, 37.59, 0)

hence, Fx = 13.68 N

Fy = 37.59 N

and for Fz:

suppose magniude of F is F.

then F (d / sqrt(c^2 + d^2)) = Fh

F (4 / sqrt(3^2 + 4^2)) = 40

F = 40 x 5 /4 = 50 N

Fz = F (c / sqrt(c^2 + d^2)) = 30 N

beta = cos^-1 ( Fy / F) = cos^-1(37.59 / 50) = 41.26 deg .......Ans