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 \(\frac{p}{q} = \frac{cos \ \beta - cos \ \alpha}{sin \ \alpha - sin \ \beta}\).