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During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the ratio of the Earth-Sun and Earth-Moon distances is closest to

1. 328
2. 382
3. 238
4. 283

Correct answer: 382

Solution

In a right triangle formed by the Earth, Moon, and Sun during the half-moon phase, the angle of 89.85° indicates that the Earth-Sun distance is significantly larger than the Earth-Moon distance. Using the sine function, the ratio of the distances can be calculated, leading to the conclusion that the closest ratio is approximately 382.

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