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A tower of height b is seen from a point O on the same horizontal level as its base, with O at a distance a from the foot of the tower. If a pole fixed on top of the tower also subtends the same angle at O, then the height of the pole is

1. b((a²-b²)/(a²+b²))
2. b((a²+b²)/(a²-b²))
3. a((a²-b²)/(a²+b²))
4. a((a²+b²)/(a²-b²))

Correct answer: b((a²+b²)/(a²-b²))

Solution

The correct option is derived from the relationship between the angles subtended by the tower and the pole at point O. By applying the tangent function to the angles and using the properties of similar triangles, we can express the height of the pole in terms of the height of the tower and the distances involved, leading to the formula b((a²+b²)/(a²-b²)}.

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