Question

The angle of elevation of a cloud from a point 60 m above a take us 30 and
dePressIon of the Reflection of clouds in the lake is 60. Don't the height of the cloud.

Answer 1

height of the cloud from surface is 120 metre

PQ / CQ = COT 30 = ROOT3

= PQ / X = ROOT3

= PQ = X ROOT 3 1

AND PQ /QD = COT 60 = 1/ ROOT 3

PQ / X+ 120 = 1/ ROOT 3

== PQ = X +120 /ROOT3 2

FROM 1 AND 2

= X ROOT 3 = X+120 /ROOT 3

===> X = 60

thus height = x +60 = 60 + 60 == 120metre

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Answer 2

Answer:

$\bf{\underline{\underline{Correct\: Question \mapsto}}}$

The of elevation of a cloud from a point 60m above a lake is 30 degree and the angle of depression of the reflection of cloud in the lake is 60 degree. find the height of the cloud.

$\bf{\underline{\underline{\pink{solution}}}}$

Let AB be the surface of the lake and H be the point of observation.

Let C be the position of the cloud above the lake and D be its reflection in the lake.

⛬ BC = BD - - - - - - - - - - - - - - (1)

AH = MB = 60m.

Let CM be x m.

CB = CM + MB - - - - - - - - - - - - (C - M - B)

CB = x + 60

⛬ CB = ( x + 60)m - - - - - - - - - - - - (2)

From (1) & ( 2) ,

BC = BD -------(Given in equation 1)

⛬ BD = ( x + 60) m - - - - - - - - - - - (3)

MD = MB +BD - - - - - - - - - (M - B - D )

MD = (60 + x + 60)m - - - - - - - - - - [from( 3 )]

⛬ MD = (x + 120) m

In right angled CHM.

tan <CHM = 30 degree = CM /HM

$\bf\frac{1}{\sqrt{3}} =\frac{x}{HM}$

$\bf\therefore{HM} = x\sqrt{3}$

In right angled DHM, tan <DHM = 60 degree = MD/ HM. - - - - - - - - - - - - - - - - - - (5)

$\bf\sqrt{3} = \frac{x + 120}{HM}$ - - - - - - - - - - - - [ from (4)]

$\bf{HM}= \frac{x + 120}{\sqrt{3}}$- - - - - - - - - - - (6)

from (5) and (6) ,

$\bf{x}\sqrt{3} =\frac{x + 120}{\sqrt{3}}$

⛬ 3x = x + 12.

⛬ 2x = 120

⛬ x = 120/2

⛬ x = 60.

The height of the cloud (CB) = (x + 60)m - - - - [from(2)] ⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀= (60 + 60 )⠀m

⟹120m⠀⠀

The height of the cloud is 120m.

$\bf{\underline{\underline{\purple{MuskaŊ}}}}$⠀⠀⠀⠀⠀⠀