60^o

90 m

A

B

C

60^o

E

?

Observer

Q. From the top of a light house, an observer looks at a ship and

finds the angle of depression to be 60^o. If the height of the light

house is 90 m then find how far is that ship from the light house.

Observe

∠EAC and ∠ACB

∠EAC and ∠ACB are what type of angles?

Alternate angles

What can we say about these two angles ?

They are equal

line of sight

Horizontal line

[Alternate angles]

Q. From the top of a light house, an observer

looks at a ship and finds the angle of

depression to be 60^o. If the height of the

light house is 90 m then find how far is

that ship from the light house.

AB

BC

90

BC

Sol.

AB represents the height of the lighthouse.

C represents the position of ship.

A represents the position of observer.

∠EAC = 60^o

∠EAC = ∠ACB

∠ACB = 60^o

In right angled ΔABC,

tan 60º =

Opposite

side

Adjacent side

Observe ∠C

Consider ΔABC

∴

∴

tan 60^o =

?

For ∠ACB

Opposite side →

Adjacent side →

AB

BC

Ratio of opposite side and Adjacent side reminds us of _________

‘tan’

Q. From the top of a light house, an observer

looks at a ship and finds the angle of

depression to be 60^o. If the height of the

light house is 90 m then find how far is

that ship from the light house.

BC =

The ship is 51.9 m far from the lighthouse.

90

BC

90

3

Sol.

BC =

BC =

∴ BC =

30

∴ BC = 51.9 m

× 1.73

∴

×

30

Now, let us rationalise the denominator

∴

∴