Question

The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30° and the angle of depression of its shadow in water of lake is 60°. Find the height of the cloud from the surface of water.
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Answer 1

Answer:

★Figure refer to attachment

Given

AC = ED

AE = CD = 60 m

BC = h = B'C

BD = B'D = 60 + h

∠BAC = 30°

∠CAB' = 60°

Find out

Find the height of the cloud from the surface of water.

$\pink{\sf \bold{Solution - }}$

★In ∆ABC★

➟ tan 30° = BC/AC

$➟ \sf \bold{\frac{1}{ √3} = \frac{h}{ AC}}$

$\sf \: ➟ AC = √3h ----(i)$

★In ∆AB'C★

➟ tan 60° = CB'/AC

➟ √3 = CD+B'D/√3h {using (i)}

$\sf \: ➟ √3 = 60 + 60 + \frac{h}{ √3h} \bold{ {Given}}$

*Cross multiplication*

➟ √3 × √3h = 120 + h

➟ 3h = 120 + h

➟ 3h - h = 120

➟ 2h = 120

$\sf \: ➟ h = \frac{120}{2} = \bold{ 60m}$

Hence,

Height of the cloud from the surface of water

➟ B'B

➟ CB + CB'

$\sf \: ➟ 60 + 60 = \red{ \bold{120 m}}$

Answer 2

So, height of the cloud from the surface of the lake

= BC = (60+x) m

= (60+60) m

= 120 m

Hence, the height of the cloud from the surface of the lake is 120 metres.

$\sf$

Answer refers in the attachment.

It helps you.