Question

The resistance of two forces which are of 130N and 90N is 150N. Calculate the angle between the two forces

Answer 1

Using the cosine rule,

$$|{\bf F_1}-{\bf F_2}|^2=F_1^2+F_2^2-2F_1F_2\cos \theta$$

we obtain

$$\cos \theta=\frac{F_1^2+F_2^2-|{\bf F_1}-{\bf F_2}|^2}{2F_1F_2}$$

$$\cos \theta=\frac{130^2+90^2-150^2}{2\times130\times90}=0.1068$$

$$\theta=84^{\circ}$$