If the angle of elevation of a cloud from a point h meeters above a la

1.	If the angle of elevation of a cloud from a point h meeters above a lake is aangle of depression of its reflection in the lake is β, prove that the height of thecloud ish (tan α+ tan β )tanß-tan α
Answer» Let a be a point h metres above the lake AF and B be the position of the cloud. Draw a line parallel to EF from A on BD at C. But, BF = DF Let, BC = m so, BF = (m + h) ⇒ BF = DF = (m + h) metres Consider ΔBAC, AB = m cosec α ---------- (1)and, AC = m cot α Consider ΔACD, AC = (2h + m) cot β Therefore, m cot α = (2h + m) cot β ⇒ m = 2h cot β / (cot α - cot β) Substituting the value of m in (1) we get, AB = cosec α [2h cot β / (cot α - cot β)] = 2h sec α / (tan β - tan α) = h (tan α + tan β)/(tan β - tan α) Hence proved. Like my answer if you find it useful!

If the angle of elevation of a cloud from a point h meeters above a lake is aangle of depression of its reflection in the lake is β, prove that the height of thecloud ish (tan α+ tan β )tanß-tan α

Answer»

Let a be a point h metres above the lake AF and B be the position of the cloud.

Draw a line parallel to EF from A on BD at C.

But, BF = DF

Let, BC = m

so, BF = (m + h)

⇒ BF = DF = (m + h) metres

Consider ΔBAC,

AB = m cosec α ---------- (1)and, AC = m cot α

Consider ΔACD,

AC = (2h + m) cot β

Therefore,

m cot α = (2h + m) cot β

⇒ m = 2h cot β / (cot α - cot β)

Substituting the value of m in (1) we get,

AB = cosec α [2h cot β / (cot α - cot β)]

= 2h sec α / (tan β - tan α)

= h (tan α + tan β)/(tan β - tan α)

Hence proved.

Like my answer if you find it useful!