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.

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