A man on the deck of a ship is 10 m above the water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30°. Calculate the distance of the cliff from the ship and the height of the cliff.
In the fig. AB is the height of the cliff.
AB = AE+EB ⇒ h+10
In ∆AED
tan 45° =
1 =
DE = h -----(1)
In ∆DEB
tan 30° =
DE = 10√3 -----(2)
From eqn. (1) and eqn. (2) we get,
h = 10√3
Height of cliff = AE+EB
= 10√3+10
= 27.32 m.
Therefore distance of the cliff from the ship is 10√3 and Height of cliff is 27.32m.