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HINT: Lets consider first what the question is asking.
The question asks us to determine the distance to the knot of Cas A that we just observed.
HINT:What information does the problem give us?
The problem tells us how haw far across the sky the knot has been observed moved in 10 years. From our previous calculation, we also know the distance traveled by the knot in that time.
HINT:What is the relationship between the information given and the
information needed?
The distance to the knot is equal to
d = L / theta Picture Hint
Where L is the distance that the object moved in 10 years, and theta is the number of degrees the object was observed to move across the sky during those years.
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?
L = 1.58 x 1012 km
theta = 3 arc seconds
HINT: Are we going to need to convert the units of any of the information that
we have gathered?
Let's use unit analysis:
d(km) = L(km)/sin(theta) ~ L(km)/theta(radians)
Since we want our answer in kilometers, we will have to convert arcseconds to radians.

3 arc-seconds * 1 radian/206,265 arcseconts = 1.45 x 10-5 radians
HINT:Plug all of the information in to the final calculation!
d = 1.58 x 1012 km / 1.45 x 10-5 = 1.1 x 1017 km

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