38. Exemplar exercise problems XIII

A ladder rests against a vertical wall at an inclination $\alpha$ to the horizontal. Its 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 $\frac{p}{q} = \frac{cos \ \beta - cos \ \alpha}{sin \ \alpha - sin \ \beta}$.