The Andromeda galaxy

The Andromeda galaxy is a giant spiral cluster of stars whose mass is that of \( 300 \) billion Suns. You can see it with the naked eye as a faint elongated cloud in the night sky. Inasmuch as it subtends an angle of \( 4.1^{\circ} \) and is known to be larger than our own galaxy [\( 163 \times 10^3 \) light-years (units of ly) in diameter for Andromeda as compared to \( 100 \times 10^3 \) light-years for our galaxy], how far away is it in light-years?

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