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A statue 1.46 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45°. The height of the pedestal (round the answer up to one decimal place), is:

Solution

✅ Correct Option: 3

Let the pedestal height be hh and the horizontal distance dd. From tan⁡45°=h/d\tan 45° = h/d we get d=hd = h. From tan⁡60°=(h+1.46)/d\tan 60° = (h+1.46)/d we get 3h=h+1.46\sqrt{3}h = h + 1.46, so h=1.46/(3−1)≈2.0h = 1.46/(\sqrt{3}-1) \approx 2.0 m.

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