From Sine Rule ${{AB} \over {\sin \theta }} = {{\sqrt {{p^2} + {q^2}} } \over {\sin \left( {\pi - \left( {\theta + \alpha } \right)} \right)}}$ $AB = {{\sqrt {{p^2} + {q^2}} \sin \theta } \over {\sin \theta \cos \alpha + \cos \theta \sin \alpha }}$ $= {{\left( {{p^2} + {q^2}} \right)\sin \theta } \over {q\sin \theta + p\cos \theta }}$ (As $\cos \alpha = {q \over {\sqrt {{p^2} + {q^2}} }}$ and $\sin \alpha = {p \over {\sqrt {{p^2} + {q^2}} }}$ )