Two forces whose magnitudes are in the ratio `3:5` give a resultant of 28N. If the angle of their inclination is `60^@`, find the magnitude of each force.

Explanation

Let ` A and B` be the two forces.
Then ` A=3 x, B=5 x ,`
` R=28 N and ` theta 60^(@)`
` Thus, ` A//B = 3//5`.
Now ` R =sqrt (A^(2) + B^(2) + 2 AB cos theta)`
:. ` 28 = Sqrt((3x) x^(2) + (5 x )^(2) (3 x) (5 x) cos 60^(@))`
or 28 sqrt(9 x^2 + 25 x^2 + 15 x^2) = 7 x`
or `x = 28//7 = 4`
:. `Forces are , A = 3 xx 4 =12 N`
and `B = 5 xx 4 = 20 N`.