UPSC CDS 1 2020 Math Paper

Given:
The top of a tower from two points at distances p and q from the base.
The base and on the same straight line are 27∘ and 63∘ respectively
Formula Used:
tan‌θ=cot(90∘−θ)
tan‌θ= Perpendicular\/Base
cot‌θ= Base ∕ Perpendicular
tan‌θ=1∕cot‌θ
BC=p and BD=q
In triangle ABD :
Tan63∘=H∕q
Tan27∘=H∕p⇒Cot27=p∕H
Now,
Tan63∘=Tan(90∘−27∘)=Cot27∘
So,
H∕q=p∕H
H2=pq
H=√pq
∴ Height of the tower is √pq