Question
A man is standing on the deck of a ship, which is 10 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.
Solution
Let C be position of the man. AB be the water level, and BH be the hill. The angles of elevation of the top and depression of foot from the deck of the ship be 60° and 30° respectively.
i.e., ∠DCH = 60° and ∠BCD = 30°
Let HD = x m
In right triangle CDH, we have
In right triangle CDB, we have
Hence, distance of the ship from the hill 
Comparing (i) and (ii), we get
Now, total height of the hill
= BD + DH = 10 + x
= 10 + 30 = 40 m
Hence, height of the hill = 40 m.
