Question

Kindly solve 43rd question!!

Answer 1

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) Hence proved.

Answer 2

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)

Hence proved.