HINT:#
The question asks us to determine the physical size of the observed remnant of Cas A.
HINT:#
The previous problem provides us with the observed size of the remanant in arc-seconds. The answer that we obtained in Cas A Activity 2, Problem 2, we know the distance to the observed object.
HINT:#
The size of the remnant
L = θ * d
Picture Hint
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.
HINT:#
θ = 350 arc-seconds
d = 1.1 x 1017 km
HINT:#
Let's use unit analysis:
L(Parsec) = θ(arc-seconds) * distance (km)
Since we want our answer in parsecs, we will have to convert arc-seconds to radians, and our distance to Parsecs.

350 arc-seconds * (1 radian/206,265 arc-seconds = 1.7 x 10-3 radians
1.1 x 1017 km * (1 Parsec/3.086 x 1013 km) = 3500 Parsec
Now, using the small angle approximation that θ = sin(θ)
L(Parsec) = θ * distance (Parsec), and our answer will have the correct units!
HINT:#
L = 1.7 x 10-3 radians * 3500 Parsecs = 5.9 Parsec
We can also express our answer in the slightly more intuitive lightyear unit by a simple conversion
5.9 Parsec * (3.262 lightyear/1 Parsec) = 19 lightyears

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