Question
From the top and foot of a tower 40 m high, the angle of elevation of the top of a light house is found to be 30° and 60° respectively. Find the height of the lighthouse. Also find the distance of the top of the lighthouse from the foot of the tower.
Solution
Let AC be the Tower such that AC = 40 m and BE be tine light house. Let CD be the horizontal from C. It is given that angles of elevation of the top of the light house from top and foot of the tower be 30° and 60° respectively.
i.e., ∠DCE = 30° and ∠BAE = 60°
Let AB = CD = x m and DE = x m
Now, in right triangle CDE, we have tan 30°
In right triangle ABE, we have
Comparing (i) and (ii), we gel
Hence,heighl of light house = BD + DE = 40 + 20 = 60 m.
In right triangle ABE, we have sin 60 
Hence, the distance of the top of the light house from the foot of the tower is 
