Two equal forces are acting at a point with an angle of `60^(@)` between them. If the resultant force is equal to `20 sqrt(3)` N, find the magnitude of each force .

Explanation

Angle between the forces , `theta = 60^(@)`
Resultant ` R = 20 sqrt(3) N, P = Q = P (say)` = ?
Resultant R ` = sqrt(P^(2) +Q^(2) + 2PQ cos theta)`
`= sqrt(P^(2) +P^(2) + 2P * P cos 60^(@))`
`= sqrt(2P^(2) + 2P^(2) + (1)/(2)) = P sqrt(3)`
`:. ` But the resultant force is ` = 20 sqrt(3)`
`:. 20 sqrt(3) = P sqrt(3)`
`P = 20 N`