UPSC CDS Math Height and Distances Questions

Let AB be the tower. Suppose BC and BD are the lengths of the shadow of the tower when sun’s elevations are 60° and 30°, respectively.
In ΔABC
tan‌60°=√3=

AB

BC

⇒BC=

AB

√3

...........(1)
In ΔABD,
tan‌30°=

1

√3

=

AB

BC+50

⇒

AB

√3

+50=√3‌AB  [Using (1)]
⇒

2‌AB

√3

=50
⇒AB=25√3m