Question

2. The angle of elevation on the top of a tower from two horizontal points at a distances of a and b from the tower are a and (900- a)?​

Answer 1

Solution :-

Let the height of the tower ‘OT’ = h

Let O be the base of tower.

Let A and B be two points on the same line through the base such that

OA = a, OB = b

∵ The angles at A and B are complementary

∴ ∠TAO = α

then ∠TBO = 90˚ – α

In rt ∠d △OAT,

tan α = OT/OA = h/a …..(i)

In rt ∠d △OBT,

tan (90˚ – α) = OT/OB = h/b

(afterwards make diagram here)

(after writing upwards before writing downwards u should make diagram of triangle. there is attached photo of diagram. )

⇒ cot α = h/b …..(ii)

Multiplying (i) and (ii) we have

tan α cot α = h/a × h/b = h2/ab

1 = h2/ab

⇒ h2 = ab

⇒ h = √ab

Hence, the height of the tower = √ab.