The tower is held in place by three cables If the force of e

The tower is held in place by three cables. If the force of each cable acting on the tower is shown, determine the magnitude of the resultant force F_R. Take x = 20 m and y = 16 m.

Solution

Angles of A ..tan A = (24÷(16^2+20^2))

A=43.188°

Angle of B... tan B =(24÷(6^2+4^2))

B=73.27°

Angle of C...tan C=(24÷(18^2+16^2))

C =44.9°

Forces in X direction...

400 cos 43.18° +800 cos 73.276° + 600 cos 44.9°

946.84

Forces in y direction

400 sin 43.18°+ 800 sin 73.27° +600 sin 44.9°

1465

Resultant force = (1465^2+946.84^2)

1744.26 N