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Two persons who are 500 metres part, observe the direction and the angular elevation of a balloon at the same instant. One finds the elevation to be 60° and the direction South-West, while the other finds the elevation to be 45° and the direction West. Then the height of the balloon is, (in meter)

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$500 \sqrt{(\frac{12 + 3 \sqrt{6}}{10})}$

$500 \sqrt{(\frac{12 - 3 \sqrt{6}}{10})}$

$250 \sqrt{3}$

$500 \sqrt{3}$

answer is A.

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