Question

7. A man standing on the deck of a ship is 10 m above water level. He observes that
the angle of elevation of the top of a cliff is 60", and the angle of depression of the
base is 30. Calculate the distance of the top of the diff from the ship and the
height of the cliff​

Answer 1

TO FIND DISTANCE OF THE TOP OF THE CLIF FROM THE SHIP AND THE HEIGHT OF THE CLIFF.

EXPLANATION.

• GIVEN

A man standing on the deck of a ship is

10 m = AB

Let CD be the hill = CD

Therefore,

AB = CD = 10 m

Angle of a elevation of the top of a cliff is 60°

and the angle of depression of the base is 30°

Therefore,

<EAD = 60°

<CAB = <BCA = 30° [ by alternate angle]

Let AD = BC = x cm

Let DE = H m

In ∆ ADE

tan ø = perpendicular / base = p / b

tan 60° = DE / AD

√3 = H / x

H = √3x ....... (1)

in ∆ABC

tan ø = perpendicular / base = p / b

tan 30° = AB / BC

1 / √3 = 10 / x

x = 10√3 m..... (2)

From equation (1) and (2)

we get,

h = √3x

h = √3 X 10√3

h = 30 m

Therefore,

Height of hill is =

CE = CD + DE = 10 + 30 = 40 m

Hence,

The height of hill is = 40 m

Distance of the hill from the ship = 10√3 m

NOTE = DIAGRAM IS ATTACHED ON IMAGE.