# 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 300. Calculate the Distance of the Cliff from the Ship and the Height of the Cliff. - Mathematics

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 300. Calculate the distance of the cliff from the ship and the height of the cliff.

#### Solution

Let H be the height of the cliff CE. And a man is standing on the ships at the height of 10 meters above from the water level.

Let AB = 10, BC = xAD = BCAB = DCDE = h

∠ACB = 30° and ∠DAE = 45°

We have tofind H and xT

The corresponding figure is as follows

In Δ ABC

=> tan C = (AB)/(BC)

=> tan 30^@ = = 10/x

=> 1/sqrt3 = 10/x

=> x = 10sqrt3

Again in ΔDAE

=> tan A = (DE)/(AD)

=> tan 45^@ = h/x

=> 1 = h/x

=> x = h

=> x = 10sqrt3

Therefore H = h + 10

=> H = 10sqrt3 + 10

=> H = 10(sqrt3 + 1)

=> H = 27.32

Hence the required distance is 10sqrt3 and height  is 27.32 m

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 12 Trigonometry
Exercise 12.1 | Q 41 | Page 32