I've seen it before - 7

Geometry Level 4

A man notices two objects in a straight line due west. After Walking a distance $x$ due north he observes that the objects subtend an angle $\alpha$ at his eye, and after walking a further distance $2x$ due north they subtend an angle $\beta$ . If the height of the man is being neglected then the distance between the objects is

Note

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\dfrac{8x}{3\cot\beta+\cot\alpha}

\dfrac{8x}{3\cot\beta-\cot\alpha}

\dfrac{8x}{3\cot\alpha-\cot\beta}

\dfrac{8x}{3\cot\alpha+\cot\beta}