Answer to Question #96968 in Physics for Bg

Question

THE RESULTANT OF TWO FORCES WHICH ARE OF MAGNITUDE 130N AND 90N IS 150N FIND THE ANGLE BETWEEN THE TWO FORCES AND FIND THE ANGLE BETWEEN THE 150N AND 130N FORCE

Answer 1

The law of cosines gives

$$150^2=90^2+130^2-2\times 90\times 130\cos(180^{\circ}-\alpha)$$

So

$$\cos(180^{\circ}-\alpha)=0.1068$$

Therefore

$$\alpha=96^{\circ}$$

The sine rule gives

$$\frac{150}{\sin(180^\circ-\alpha)}=\frac{90}{\sin(\theta)}$$

So

$$\sin(\theta)=\frac{90}{150}\times\sin(84^\circ)=0.5967$$

Finally

$$\theta=37^{\circ}$$