# Q.15 A ladder against a vertical wall at an inclination $\alpha $ to the horizontal .The foot is pulled away from the wall through a distance p, so that its upper end slides a distance q down the wall and then the ladder makes an angle $\beta $ to the horizontal . show that p /q = $\mathrm{cos}\beta -\mathrm{cos}\alpha /\mathrm{sin}\alpha -\mathrm{sin}\beta $

Dear student

The given information can be represented diagrammatically as

In the above figure AB and CD represent the same ladder

So, their length must be equal

Let length of the ladder be

*h*∴ AB = CD =

*h*Hence, proved

Regards

**
**