Question

Ram and Shyam are 10 km apart. They both see a hot-air balloon making angles of elevation \(60^\circ\) and \(30^\circ\) respectively. What is the height at which the balloon could be flying?

• A. \(4\sqrt{3}\)
• B. \(5\sqrt{3}\)
• C. \(3\sqrt{3}\)
• D. \(2\sqrt{3}\)

Hint:

In height–distance problems with two angles from points on a line, the larger angle corresponds to the nearer observer}. Set up distances accordingly and use \(\tan\theta\).