Question

the angle elevation of cloud from a point of 60 m above a lake is 30 degrees and the angle of depression of the reflection of the cloud in the lake is this 60 degrees. find the height of the cloud from the surface of the lake .​

Answer 1

Answer:

Step-by-step explanation:

Sorry for the handwriting

Answer 2

$\huge\mathfrak\pink{Solution :-}$

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

$\therefore \rm CB = h + 60 m∴CB=h+60m$

$\rm In \: \triangle \: CPMIn△CPM$

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

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

$\rm ➨ PM = \sqrt{3} h.......(i)➨PM=$

$\rm In \: \triangle \: PMC,In△PMC,$

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

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

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

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

$\rm☄from \: eq(i) \: and \: eq(ii)$

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

$\rm \implies3h = h + 120m⟹3h=h+120m$

$\rm \implies3h - h= 120m⟹3h−h=120m$

$\rm \implies2h = 120⟹2h=120$

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

$\rm \implies h = 60m⟹h=60m$

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

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

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