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) \(3: 1\)
View Dynamic Solution & Explanation ▼
Correct Solution: Option D
Step-by-step Solution:
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)\[\]
