ABC is a triangular park with AB = AC = 100 meters. A clock

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ABC is a triangular park with AB = AC = 100 meters. A clock tower is situated at the mid-point of BC. The angles of elevation of the top of the tower of A and B are cot^-1 (3.2) and cosec^-1(2.6) respectively. The height of the tower in meters is ?

1. 25/2
2. 25
3. 50
4. None of these

Correct Option: B

Let us draw a figure below as per given question.
Given ∝ = cot^-1 (3.2) and β = cosec^-1(2.6)
In triangle ΔPAD, AD = h cot ∝
In triangle ΔPBD, BD = h cot β
In triangle Δ ABD,
AB² = AD² + BD²
= h²(cot²∝ + cot² β )
⇒ 100² = h²{ cot² ∝ + (cosec² β - 1) }
⇒ 100²= h² { (3.2)² + (2.6)² - 1} = 16h²
⇒ h = 25 m.