Math, asked by pk966317, 10 months ago

the angle of elevation of a cloud from a point 60 metre above a lake is 30° and angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud from the surface of the lake​

Answers

Answered by raksha54devi
5

Answer:

120 m

Step-by-step explanation:

most of the question is explained in figure itself and the easiest way of doing such questions is that what the height is given , your answer will be twice of that

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Answered by ꜱɴᴏᴡyǫᴜᴇᴇɴ
77

\huge\mathfrak\pink{Solution :-}

Let AB be the surface of the lake and P be the point of observation such that AP = 60 m.

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

Then CB =

\rm Draw \: PM \perp CBDrawPM⊥CB

Let CM = h

\therefore \rm CB = h + 60 m∴CB=h+60m

\rm In \: \triangle \: CPMIn△CPM

\rm \tan30 \degree = \frac{CM}{PM}tan30°=

\rm ➨ \frac{1}{ \sqrt{3} } = \frac{h}{PM}➨

\rm ➨ PM = \sqrt{3} h.......(i)➨PM=

\rm In \: \triangle \: PMC,In△PMC,

\rm ➨\tan60 \degree = \frac{C ' M}{PM}➨tan60°=

\rm ➨ \tan60 \degree = \frac{C'B + BM}{PM}➨tan60°=

\rm ➨ \sqrt{3} = \frac{h + 60m + 60m}{PM}➨

\rm ➨ \sqrt{3} = \frac{h +120m}{PM} .......(ii)➨

\rm☄from \: eq(i) \: and \: eq(ii)

\rm ➨ \sqrt{3}h = \frac{h + 120m}{ \sqrt{3} }➨

\rm \implies3h = h + 120m⟹3h=h+120m

\rm \implies3h - h= 120m⟹3h−h=120m

\rm \implies2h = 120⟹2h=120

\rm \implies h = \frac{ \cancel{120}}{ \cancel{2} } = 60m⟹h=

\rm \implies h = 60m⟹h=60m

\rm ➯ CB = h + 60m = 60m + 60m = 120m➯CB=h+60m=60m+60m=120m

⇾ \rm Thus,the \: height \: of \: the \: cloud

\: from \: the \: surface \:of \: lake \boxed{ \rm120m.}

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