The question asks us to determine the physical size of the Andromeda Galaxy.
L = θ * d
Where θ is angular size of the observed object and d is the distance from the observation to that object.
NOTE: This formula uses the approximation that when angle θ is small, sin(θ) ≈ θ.
d = 2 x 106 lightyears
L(lightyears) = θ° * distance(lightyears)
Since we want our answer in lightyears, we will have to convert degrees to radians (to satisfy the requirements for the assumption that sin(θ) is approximately equal to θ).
θ = 3° * 2π/360° = 0.052 rad;
So, L(lightyears) = theta * distance(lightyears), and our answer will have the correct units!
This is very roughly the same size as the Milky Way!
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