A ladder rests against a vertical wall at an angle α to the...

Let, the length of the ladder be $l and AB is the wall.<br /><img src="/api/proxy-image?url=https$∴ AD = EC = l$<br />Now,$BE - BD = 2$<br />$⇒ lcos \beta - lcos \alpha = 2$<br />$⇒ l\left(cos \beta - cos \alpha\right) = 2$<br />$⇒ 2lsin \dfrac{\alpha + \beta}{2}sin \dfrac{\alpha - \beta}{2} = 2 \ldots \ldots \left(i\right)$<br />Also,$BA - BC = 5$<br />$⇒ lsin \alpha -lsin \beta ==l\left(sin \alpha -$sin$\beta\right) =5$<br />$⇒ 2lcos \dfrac{\alpha + \beta}{2}$sin$\dfrac{\alpha - \beta}{2} =5 \ldots \ldots \left(ii\right)<br />Dividing equation \left(i\right) & \left(ii\right), we get,<br />∴ tan $\dfrac{\alpha + \beta}{2} = \dfrac{2}{5}$