Question

Two equal forces are acting at a point with an angle of 60° between them. If the resultant force is equal to 20√3 N, find the magnitude of each force.

Answer 1

if two equal forces acting at a point with an angle Ф then magnitude of resultant force is 
= 2Fcos(Ф/2)
20√3 = 2Fcos(60/2)
10√3 = F√3/2
F = 20 N
hence magnitude of each force = 20 N

Answer 2

resultant = $\sqrt{A^2+B^2+2ABcos \alpha }$ where angle between two forces is α.....
here α is 60* and both A and B are equal...let them be x....

$\sqrt{x^2+x^2+2x^2cos60}$ = 20√3
2x²+2x²(1/2) = 1200
3x²              = 1200
x²                = 400
x                 = 20
therefore magnitude of each of the forces is 20N...
thanks for reading......:)