Let A and B be two towers with same base. From the midpoint of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 60°, respectively. The ratio of the heights of B and A is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 3 : 1.
Let the midpoint of the line joining the bases of the towers be O. Now since it is the midpoint, hence the distance from the bases of both the towers will be the same, say x
Now for tower A in △PQO,
⇒ tan 30º= PQ/OQ
⇒ 1/√3 = A/x ....... (i)
Similarly for tower B in △SRO
⇒ tan 60º = RS/OR
⇒ √3 = B/x ..........(ii)
Now taking equation (ii)/(i)
⇒ B/x : A/x :: √3/1 : 1/√3
⇒ B : A = √3 × √3 : 1
⇒ B : A = 3 : 1