JEE-Mains 2015 (27/30)

Geometry Level 3

If the angles of elevation of the top of a tower from three collinear points $A, B,$ and $C$ , on a line leading to the foot of the tower, are $30^{\circ},45^{\circ},$ and $60^{\circ},$ respectively, then the ratio $AB:BC$ is $\text{\_\_\_\_\_\_\_\_\_\_}.$