Geometry

Trigonometry

Medium

The angle of elevation of the top of a tower from a point is 30°. When the observer moves 50 meter closer, the angle becomes 60°. Find the height of the tower.

25√3 meter

50 meter

50√3 meter

25 meter

✅ Correct Option: 1

Let the height be $h$ and the nearer distance be $x$ .

From the nearer point, $\tan 60^\circ = h/x$ , so $h = x\sqrt{3}$ .

From the farther point, $\tan 30^\circ = h/(x+50)$ , so $h = (x+50)/\sqrt{3}$ .

Equating, $3x = x + 50$ , so $x = 25$ and $h = 25\sqrt{3}$ metres.

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Solution

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