Question

Determine by resolution of forces the resultant of the following three coplanar forces acting at a point: 200 N acting at 20° to the horizontal; 400 N acting at 165° to the horizontal; 500 N acting at 250° to the horizontal.

Answer 1

A tabular approach using a calculator may be made as shown below:

Horizontal component

Force 1	200 cos 20°	= 187.94
Force 2	400 cos 165°	= −386.37
Force 3	500 cos 250°	= −171.01
	Total horizontal component	= −369.44

Vertical component

Force 1	200 sin 20°	= 68.40
Force 2	400 sin 165°	= 103.53
Force 3	500 sin 250°	= −469.85
	Total vertical component	= −297.92

The total horizontal and vertical components are shown in Figure (a).

Thus the resultant of the three forces given is 474.6 N acting at an angle of −141.12° (or +218.88°) to the horizontal.