UPSC NDA Math Model Paper 4

It can be noted that the angle of elevation from closer points is more than the angle from farther points.
The position of the three points is shown in the following diagram:
Using the definition of trigonometric ratio tan θ:
AP=

QP

tan‌30°

=√3QP
BP=

QP

tan‌45°

=QP
CP=

QP

tan‌60°

=

QP

√3

It is given that BC=60m.
⇒BP−CP=60
⇒QP−

QP

√3

=60
⇒QP=

60√3

√3−1

Now,AB=AP−BP
=√3QP−QP
=QP(3−1)
=

60√3

√3−1

(√3−1)
=60√3m