Help for solving heights and distances ( trignometry) question

[shivansh]

The angles of elevation of a tower H meter high from points A and B are α and β respectively. An airplane is flying at a height greater than that of the tower and is descending towards the tower. If the angle of elevation of the airplane from point B is θ and the speed of the airplane is 500km/hr.
Prove that
Time taken for impact of the airplane and the tower is
H² [tanθ (tanα + tanβ) – (tanαtanβ) + tan²β] / 500 tan²α tan²β

 

[shivansh]

dennis the question which i posted is made by me. I wanted to check if some is able to prove it

 

[Ishuda]

The angles of elevation of a tower H meter high from points A and B are α and β respectively. An airplane is flying at a height greater than that of the tower and is descending towards the tower. If the angle of elevation of the airplane from point B is θ and the speed of the airplane is 500km/hr.
Prove that
Time taken for impact of the airplane and the tower is
H² [tanθ (tanα + tanβ) – (tanαtanβ) + tan²β] / 500 tan²α tan²β

If that is the totality of the statement, it may be true for some \(\displaystyle \alpha, \beta, and\space \theta\) in a particular situation, but it is not true for that same \(\displaystyle \alpha, \beta, and\space \theta\) in all situations.