Question

A ladder rests against a wall at an angle α to the horizontal. Its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal. Show that

$\frac{a}{b}=\frac{\cos \alpha -\cos \beta }{\sin \beta -\sin \alpha }$

Answer 1

Let be the ladder such that its top is on the wall and bottom is on the ground. The ladder is pulled away from the wall through a distance a, so that its top slides and takes position. So

And. Let

We have to prove that

We have the corresponding figure as follows

We use trigonometric ratios.

In

And

Again in

And

Now,

And

So

Hence .