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.

Answer 1

Let AB be the height of the hill.

In right-angled ΔBCD,

`"CD"/"DB" = tan 30°` 

⇒ DB = 10√3 m.

In right-angled ΔAMC,

`"AM"/"CM" = tan 60°`  

⇒ AM = √3 CM

⇒ AM = √3 DB = √3 x 10√3 = 30 m

Thus,
AB = AM + MB
AB = (30 + 10) m = 40 m

∴ Height of the hill be 40 m.