Geometry

Trigonometry

Medium

On the level ground, the angle of elevation of a tower is $30°$ . On moving 20 m nearer, the angle of elevation is $60°$ . The height of the tower is:

$5\sqrt{3}$ m

$10\sqrt{3}$ m

$15\sqrt{3}$ m

$20\sqrt{3}$ m

✅ Correct Option: 2

Let the height be $h$ . From the farther point, distance $= h\cot 30° = h\sqrt{3}$ ; from the nearer point, distance $= h\cot 60° = h/\sqrt{3}$ . Their difference is 20, so $h\sqrt{3} - \frac{h}{\sqrt{3}} = 20 \Rightarrow \frac{2h}{\sqrt{3}} = 20 \Rightarrow h = 10\sqrt{3}$ m.

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On the level ground, the angle of elevation of a tower is 30°30°30°. On moving 20 m nearer, the angle of elevation is 60°60°60°. The height of the tower is:

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CUET General Test Past Year Questions (Topic-Wise)

On the level ground, the angle of elevation of a tower is $30°$ . On moving 20 m nearer, the angle of elevation is $60°$ . The height of the tower is: