Question

Three tensional forces are acting on an object.
F1 = 60N, 60

Answer 1

The sum of the forces is the vector sum. The easiest way to do it is to find the x- and y-components and their sum, and then find the resultant R by the Pythagorean theorem. We assume the angle is counted from the positive direction of x-axis counterclockwise. In this case:

$$F_{1x}=60\cos60°=30\text{ N},\\ F_{1y}=60\sin60°=52\text{ N}.\\ R_{x}=F_{1x}+F_{2x}+F_{3x},\\ R_y=F_{1y}+F_{2y}+F_{3y}.\\ R=\sqrt{R_x^2+R_y^2}.$$