The sum of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is perpendicular to  minimum force then the forces are

Let say A is the smaller force.A+B=16 (given)                          ........(i)tan⁡ϕ=Bsin⁡θA+Bcos⁡θ=tan⁡90∘∴ A+Bcos⁡θ=0⇒cos⁡θ=−AB ........(ii)8=A2+B2+2ABcos⁡θ                    ........(iii)By solving eqs (i), (ii) and (iii) we get A = 6 N, B = 10 N