Question

Two forces make an angle of 60degree . The magnitude of one of the forces is 4N and that of the resultant is 6N . Find the magnitude of the other force.

Answer 1

$$\begin{gathered} Magnitudeofthefirstforce=f_1=4N \\ resul\tan t=6N \\ letsecondforceis{f}_2 \\ anglebetween{f}_{1}and{f}_{2}is60degree \\ R=\sqrt{{f_1}^2+{f_2}^2+2f_1{f}_2\cos \theta } \\ 6=\sqrt{{f_1}^2+16+8f_1\cos 60} \\ 36={f_1}^2+16+4f_1 \\ {f_1}^2+4f_1-20=0 \\ {f}_1=\frac{-4\pm \sqrt{16+80}}{2} \\ {f}_1=\frac{-4\pm 9.7}{2} \\ {f}_1=-6.85Nor2.85N \end{gathered}$$