GATE Chemical 2024 | GA | Question: 10

Question

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 $89.85^{\circ}$, the ratio of the Earth-Sun and Earth-Moon distances is closest to

• A. $328$
• B. $382$
• C. $238$
• D. $283$

Answer 1

• At half-moon: ∠M = 90°, ∠E = 89.85°, so ∠S = 0.15°. (Sum of triangles = 180°)

• By sine rule:

  ES/ EM =1/ sin⁡(0.15°) 

• sin(0.15°)≈0.002618.

• Hence Ratio:

  ES / EM ≈1 / 0.002618 ≈ 382

✅ Earth–Sun is about 382 times Earth–Moon.