There are two poles, one on each side of the road. The higher pole is 54 m high. From the top of this pole, the angle of depression of the top and bottom of the shorter pole is 30 and 60 degrees respectively. Find the height of the shorter pole.

Let the longer pole to be CD and the shorter pole to be AB.
Angle of depression from C to A i.e. angle YCA is 30 degrees which means that angle CAX = 30 degrees.
Angle of depression from C to B i.e. angle YCB is 60 degrees which means that angle CBD = 60 degrees.
Tan CBD = CD/BD where CD = 54 m.
This gives BD = $$\frac{54}{\sqrt{\ 3}}=18\sqrt{\ 3}$$.
In triangle CAX, Tan CAX = CX / AX where Ax = BD = $$\frac{54}{\sqrt{\ 3}}=18\sqrt{\ 3}$$.
This gives CX = 18 m. XD = CD - CX = 36 m.
Height of the shorter pole i.e. AB is equal to XD and thus the correct answer is Option B.