The shadow of a tower standing on a level ground is found to be 60 metres longer when the sun's altitude is $30^{\circ}$ than when it is $45^{\circ}$. The height of the tower is :

Question

( A ) $90m$
( B ) $30m$
( C ) $60 \sqrt{3}m$
( D ) $30(\sqrt{3} + 1)m$