GATE 2024 CH – Question 10
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
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Correct answer: (B) 382
Explanation
The right angle is at the Moon. With the angle at the Earth equal to $89.85°$, $\cos 89.85° = \frac{\text{Earth-Moon}}{\text{Earth-Sun}}$, so the ratio is $\frac{1}{\cos 89.85°} = \frac{1}{\sin 0.15°} = \frac{1}{0.002618} = 382$.