Question

the angle of elevation of a cloud from a point h metres above the surface of a lake is theta and the angle of depression of its reflection in the lake is Φ.Prove that the height of the cloud above the lake is h (tan Φ + tan theta) / (tan Φ - tan theta) .......answer only if you know..... ​

Answer 1

Let AN be the surface of the lake and O be the point of observation such that OA = h metres.

Let P be the position of the cloud and P' be its reflection in the lake

Then PN = P'N

Let OM ⊥ PN

Also, ∠POM = α and ∠P'OM = β

Let PM = x

Then PN = PM + MN = PM + OA = x + h

In rt. ΔOPM, we have

In rt. ΔOMP', we have,

Equating (1) and (2):

Hence, height of the cloud is given by PN = x + h

Hence proved

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Answer 2

Answer:

a pair of linear equation can be solved by substitution, elimination and cross multiplication method