Question

Three forces P,Q & R are acting at a point in the plane . the angle between P & Q and Q & R are 150° & 120° respectively , then for equilibrium forces P,Q & R are in the ratio

Answer 1

$$\begin{gathered} \mathrm{For}\mathrm{equilibrium}: \\ \frac{\mathrm{P}}{\mathrm{sinp}}=\frac{\mathrm{Q}}{\mathrm{sinq}}=\frac{\mathrm{R}}{\mathrm{sinr}} \\ \mathrm{where} \\ \mathrm{p}=\mathrm{Angle}\mathrm{between}\mathrm{Q}\&\mathrm{R}={120}^{\mathrm{o}} \\ \mathrm{r}=\mathrm{Angle}\mathrm{between}\mathrm{P}\&\mathrm{Q}={150}^{\mathrm{o}} \\ \mathrm{q}=\mathrm{Angle}\mathrm{between}\mathrm{P}\&\mathrm{R}={360}^{\mathrm{o}}-\left({120}^{\mathrm{o}}+{150}^{\mathrm{o}}\right) \\ ={90}^{\mathrm{o}} \\ \mathrm{Hence}, \\ \mathrm{P}:\mathrm{Q}:\mathrm{R}=\mathrm{sinp}:\mathrm{sinq}:\mathrm{sinr} \\ =\frac{\sqrt{3}}{2}:\frac{1}{2}:\frac{1}{1} \\ =\sqrt{3}:1:2 \end{gathered}$$