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.
[CBSE Delhi 2017] ​

Answer 1

★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.

Solution

★In ∆ABC★

➟ tan 30° = BC/AC

➟ 1/√3 = h/AC

➟ AC = √3h ----(i)

★In ∆AB'C★

➟ tan 60° = CB'/AC

➟ √3 = CD+B'D/√3h {using (i)}

➟ √3 = 60 + 60 + h/√3h {Given}

*Cross multiplication*

➟ √3 × √3h = 120 + h

➟ 3h = 120 + h

➟ 3h - h = 120

➟ 2h = 120

➟ h = 120/2 = 60m

Hence,

Height of the cloud from the surface of water

➟ B'B

➟ CB + CB'

➟ 60 + 60 = 120 m

$\rule{200}3$

Answer 2

Let AO=H

CD=OB=60m

A'B=AB=(60+H)m

In triangke AOD,

tan30'=AO/OD=H/OD

H=OD/√3

OD=√3 H

Now, in triangle A'OD,

tan60'=OA'/OD=(OB+BA')/OD

√3=(60+60+H)/√3 H

    =(120+H)/√3 H

 =>120+H=3H

      2H=120

       H=60m

Thus, height of the cloud above the lake = AB+A'B

                                                                 =(60+60)

                                                                  =120m

❤️