UPSC CDS 2 2021 Math Paper

Let OQ be a ladder.
∴OQ=10m
Some part of Flagstaff QR=10m
Now, QR=QO=10m
So, ln∆OPR⇒∠R=30∘
∵OR=OQ
⇒∠ROQ=∠ORQ
Let PQ=h ‌∵tan‌60∘=‌

PR

OP

⇒‌‌√3=‌

10+h

OP

⇒‌‌OP=‌

10+h

√3

. . . (ii)
‌∵tan‌30∘=‌

h

OP

⇒‌‌OP=‌

h

(1∕√3)

=√3h . . . (ii)
From Eq. (i) and Eq. (ii), we get
‌

10+h

√3

=√3h⇒10+h=3h
⇒10=2h
⇒h=5m
Height of flagstaff
=h+10=5+10=15m
Hence, the height of the flagstaff is 15m.