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HINT: Lets consider first what the question is asking.
The question asks us to determine the physical size of the observed remnant of Cas A.
HINT:What information does the problem give us?
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:What is the relationship between the information given and the
information needed?
The size of the remnant
L = theta * d
Picture Hint
Where theta is angular size of the observed object and d is the distance from the observation to that object.
Note that this formula uses the approximation that when an angle theta is small, the sin of that angle is approximately equal to that angle (in radians).
HINT:What information do we need to plug into the relationship?
theta = 350 arc-seconds
d = 1.1 x 1017 km
HINT: Are we going to need to convert the units of any of the information that
we have gathered?
Let's use unit analysis:
L(Parsec) = theta(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 theta = sin(theta)
L(Parsec) = theta * distance (Parsec), and our answer will have the correct units!
HINT:Plug all of the information in to the final calculation!
L = 1.7 x 10-3 * 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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