Question
From the top of a tower the angles of depression of two objects on the same side of the tower are found to be α and β (α > β). If the distance between the objects is p metres,
show that the height It of the tower is given by h = 
Also, determine the height of the tower if p = 50 metres, α = 60°, β = 30°.
Solution
Case I : Let AB be the tower whose height is h metres. D arid C are the position of two objects which are p metres apart from each other. The angles of depression of two objects D and C from the top of the tower be β and α respectively.
i.e., ∠BDA = β and ∠BCA = α
In right triangle ABC, we have
In right triangle ABD, we have
Comparing (i) and (ii), we get
Case II : p = 50 m, α = 60°, β = 30°.
= 20 x 1.732 = 43.25 m.
Hence, height of the tower is 43.25 m.
