Question

The angle of elevation of a cloud from a point h meters above lake is alpha . The angle of depression of its reflection is 45degree . Find the height of the cloud

Answer 1

Step-by-step explanation:

Let C be the cloud and C' be its reflection. Let the height of the cloud be H metres.

BC=BC'=H m

Now BM=AP= h m, therefore, CM= H-h and MC' = H+h

In CPM,

= tan

… (i)

In PMC',

… (ii)

From (i) and (ii),

Htan - htan = Htan+htan

Htan - Htan = htan + htan

H(tan - tan) = h(tan+tan)

Hence, the height of the cloud is metres.

OR

Let B be the window of a house AB and let CD be the other house. Then, AB = EC = h metres.

Let CD = H metres. Then, ED= (H-h) m.

In BED,

cot =

BE = (H-h) cotα … (i)

In ACB,

cot =

AC=h.cot … (ii)

But BE=AC

(H-h) cot = hcot

H=

H = h(1+tan cot)

Thus, the height of the opposite house is h(1+tancot) metres.