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GATE 2024 XH2 (English) – Question 10

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

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

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Correct answer: (B) 382

Explanation

The right angle is at the Moon. The Earth-Moon side is adjacent to the angle at Earth and the Earth-Sun side is the hypotenuse, so $\frac{ES}{EM} = \frac{1}{\cos 89.85^\circ} = \frac{1}{\sin 0.15^\circ} = \frac{1}{0.002618} \approx 382$.