Question

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 diff is 45° and the angle of depression of the base is 30°. Find the distance of the diff from the ship and the height of the cliff. 

Answer 1

Let B be the position of the man, D the base of the cliff, x be the distance of cliff from the ship and h + 10 be the height of the hill. ∠ABC = 45° and ∠DBC = 30°
Therefore, ∠BDE = 30° 

In ΔABC,

`tan45^circ = "AC"/"BC"`

⇒ `"h"/"x" = 1`

⇒ h = x   (1)

In ΔBED,

`tan 30^circ = "BE"/"ED"`

⇒ `1/sqrt(3) = 10/"x"`

⇒ x = `10sqrt(3) = 10 xx 1.732 = 17.32`

Thus , the distance of the diff from the ship is 17.32 m.

From (1),
h = x = 17.32

∴ Height of the diff = 17.32 + 10 = 27.32

Thus , the height of the diff is 27.32 m.