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(C) Let the tower be $AB$ with height $h$. Let the two points on the horizontal plane be $C$ and $D$ such that $BC = b$ and $BD = a$. Given that the a

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$\sqrt{ab}$

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(C) Let the tower be $AB$ with height $h$. Let the two points on the horizontal plane be $C$ and $D$ such that $BC = b$ and $BD = a$. Given that the angles of elevation from $C$ and $D$ are $\alpha$ and $90^\circ - \alpha$ respectively. In $\Delta ABC$,$	an \alpha = \frac{AB}{BC} = \frac{h}{b} \implies h = b 	an \alpha$ ... $(i)$ In $\Delta ABD$,$	an(90^\circ - \alpha) = \frac{AB}{BD} = \frac{h}{a} \implies \cot \alpha = \frac{h}{a} \implies h = a \cot \alpha$ ... (ii) Multiplying equations $(i)$ and (ii): $h^2 = (b 	an \alpha)(a \cot \alpha) = ab 	an \alpha \cdot \frac{1}{	an \alpha} = ab$ Therefore,$h = \sqrt{ab}$.

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