Answer:
x is approximately 95.495
Explanation:
The given information are;
One lunar month = 30 days
The measured time between the first and third quarters = 14.9 days
Therefore, the angle of rotation for 30 days = 360°
The angle of rotation for 14.9 days = 14.9×360/30 = 178.8°
Therefore, whereby 2·θ = 178.8°
θ = 178.8°/2 = 89.4°
Therefore, given that the angle at the tangent from Sun to the Moon = 90°, we have;
The angle between the line from the Sun to the Moon = 90° - 89.4° = 0.6°
From sine rule, we have;
1/(sin 0.6) = x/(sin 90°)
x = (sin 90°)/(sin 0.6°) ≈ 95.495
x = 95.495.
