Question 6

Mathematics Trigonometry Simple Identities Medium

If two towers of heights \(h_{1}\) and \(h_{2}\) subtend angles \(60^{\circ}\) and \(30^{\circ}\) respectively at the mid point of the line joining their feet, then \(h_{1}: h_{2}\) is

(A) \(1: 2\)
(B) \(1: 3\)
(C) \(2: 1\)
(D) \(3: 1\)
✓ Correct Answer: Option D Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Heights of the two buildings are \(h_{1}\) and \(h_{2}\) \[\] \( \frac{h_{1}}{x}=\sqrt{3} \Rightarrow x=\frac{h_{1}}{\sqrt{3}} \) \[\] \( \frac{h_{2}}{x}=\frac{1}{\sqrt{3}} \Rightarrow \mathrm{x}=\sqrt{3} h_{2} \) \[\] \( \frac{h_{1}}{\sqrt{3}}=\sqrt{3} h_{2} \Rightarrow \frac{h_{1}}{h_{2}}=\frac{3}{1}\)\[\]Choice (D)\[\]

Solution Explanation Image

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