Question

The angle of elevation of a cloud from a point 120 m above a lake is 30 degrees and the angle of depression of its reflection in the lake is 60 degrees. Find the height of the cloud

Answer 1

Answer:

The height of cloud is 240 m

Step-by-step explanation:

Refer the attached figure

Let the height of cloud be H i.e. CE

Height = Length of image

So, CD =EF = H

AB = DE = 120 m

CD = CE - DE = H - 120

FD = FE+DE =H+120

In ΔBCD

$tan\theta = \frac{Perpendicular}{Base}$

$tan30^{\circ} = \frac{CD}{BD}$

$\frac{1}{\sqrt{3}}= \frac{H - 120}{BD}$

$BD= \frac{H - 120}{\frac{1}{\sqrt{3}}}$  --- 1

In ΔBDF

$tan\theta = \frac{Perpendicular}{Base}$

$tan60^{\circ} = \frac{DF}{BD}$

$\sqrt{3} = \frac{H+120}{BD}$

$BD = \frac{H+120}{\sqrt{3}}$ --- 2

Equate 1 and 2

$H+120=3( H - 120)$

$H+120=3H -360$

$480=2H$

$240=H$

Hence The height of cloud is 240 m

Answer 2

Answer: refer the pic uploaded