Two forces whose magnitude 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=3x,B=5x,R=28N` and `theta=60^(@)`
Thus `A/B=3/5`
Now `R=sqrt(A^(2)+B^(2)+2ABcos theta)`
`:.28=sqrt((3x)^(2)+(5x)^(2)+2(3x)(5x)cos 60^(@))`
or `28=sqrt(9x^(2)+25x^(2)+15x^(2))=7x` or `" "x=28/7=4`
`:.` Forces are `A=3xx4=12N` and `B=5xx4=20N`