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 `F_(1)` and `F_(2)` be the two forces.
Then `F_(1)=3x,F_(2)=5x,R=28N` and `theta=60^(@)`
`R=sqrt(F_(1)^(2)+F_(2)^(2)+2F_(1)F_(2)cos theta`
` rArr 28=sqrt((3x)+(5x)^(2)+2(3x)(5x)cos 60^(@)`
`rArr 28=sqrt(9x^(2)+25x^(2)+15x^(2))=7x`
`rArr x=28/7=4`
`:. F_(1)=3xx4=12N,F_(2)=5xx4=20N`.