SSC CHSL 2024 PYQ — Question 22

The correct answer is option 1 i.e. $5\sqrt{3}$

Given that

The angles of elevation of 60° and 30°, respectively, from two different observation points P and Q. 

The distance between P and Q is 10 m

Let the height of pole be H

According to the question

PQ = 10 m, 

So, In triangle APO ,

⇒ tan 60º = H/OP

⇒ $\sqrt3$ = H/OP

⇒ OP = H/$\sqrt3$ m

In triangle AOQ,

⇒ tan 30º = H/OQ

⇒1/$\sqrt3$ = H/OQ

⇒ OQ = H$\sqrt3$ m

As we seen, OQ - OP = PQ

⇒  H$\sqrt3$ -  H/$\sqrt3$  = 10

⇒ 3H - H = 10$\sqrt3$

⇒ 2H = 10$\sqrt3$

⇒ H = 5$\sqrt3$ m