Question : The respective ratio between the height of the tower and the point at some distance from its foot is $5\sqrt{3}:5$. What will be the angle of elevation of the top of the tower?
Option 1: 30°
Option 2: 60°
Option 3: 90°
Option 4: 45°
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Correct Answer: 60°
Solution :
It is given that the respective ratio between the height of the tower and the point at some distance from its foot is $5\sqrt{3}:5$.
So, AB : BC = $5\sqrt{3}:5$
In ΔABC,
$\frac{AB}{BC}=\tan\theta$
⇒ $\frac{5\sqrt{3}}{5}=\tan\theta$
⇒ $\tan\theta=\sqrt{3}$
$\therefore \theta=60°$
Hence, the correct answer is 60°.
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