Two concurrent forces 30N and 40N are acting at an angle of `60^(@)` with respect to each other. Calculate the magnitude and direction of the resultant.

Explanation

Given : P=30N, Q=40N, Q=`60^(@),sin60^(@)=0.866`
Magnitude of the resultant, `cos60^(@)=0.5`
`R=(P^2+Q^2+2PQcostheta)^(1//2)`
`=(30^2+40^2+cancel(2)xx30xx40xxcancelcos60^(@))^(1//2)=(900+1600+1200)`
`=60.83N`
The direction of the resultant 'R' with `vecP`
`prop=tan^(-1)((Qsintheta)/(P+Qcostheta))=tan^(-1)((40xx0.866)/(30+40xx0.5))`
`tan^(-1)(0.6892)`
`prop=34^(@)34` w.r.t `vecP`