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?

Solution(By Examveda Team)

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