The sides of the triangle are $\sin \alpha, \cos \alpha$ and $\sqrt{1 + \sin \alpha \cos \alpha}$ for some $0 < \alpha < \frac{\pi}{2}$. Then the greatest angle of the triangle is

Question

( A ) $120^{\circ}$
( B ) $60^{\circ}$
( C ) $150^{\circ}$
( D ) $90^{\circ}$