The angles of depression and elevation of the top of a wall 11 m high from top and bottom of a tree are 60° and 30° respectively. What is the height of the tree?

Answer: Option B

Let DC be the wall, AB be the tree.
Given that ∠DBC = 30°, ∠DAE = 60°, DC = 11 m
$$\begin{array}{rl}& \tan 30^{\circ }=\frac{DC}{BC}\\ & \frac{1}{\sqrt{3}}=\frac{11}{BC}\\ & BC=11\sqrt{3}m\\ & AE=BC=11\sqrt{3}m.....\left(1\right)\\ & \tan 60^{\circ }=\frac{ED}{AE}\end{array}$$
$$\sqrt{3}=\frac{ED}{11\sqrt{3}}$$   [∵ Substituted value of AE from (1)]
$$\begin{array}{rl}& ED=11\sqrt{3}\times \sqrt{3}\\ & =11\times 3\\ & =33\\ & \text{Height}\text{of}\text{the}\text{tree}\\ & =AB=EC=\left(ED+DC\right)\\ & =33+11\\ & =44\text{m}\end{array}$$