If you saw Comet Halley when it was 0.9 AU from Earth and it had a visible tail 6° long, how long was the tail
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If you saw Comet Halley when it was 0.9 AU from Earth and it had a visible tail 6° long, how long was the tail

[From: ] [author: ] [Date: 12-04-20] [Hit: ]
If the angular extent is θ,2 Tan(θ/2)= extent/distance.2 Tan(θ/2)≈ 2.(θ/2)= θ = π/30 Radian.extent = distance X (π/30)= 0.9AU X (π/30)= 0.......
Convert degrees to Radians first.
6° = 6 [π/180] = π/30 Radian.
If the angular extent is θ, the ratio to the extent to distance is
2 Tan(θ/2)= extent/distance.
As this is a small angle
2 Tan(θ/2)≈ 2.(θ/2)= θ = π/30 Radian.
extent = distance X (π/30)
= 0.9AU X (π/30)
= 0.03 π
= 0.09425 AU
= 14,137,167 km = length of the tail

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That was all they gave.

Well, whoever wrote that problem for you oversimplified it. Anyway, I suggest that you DRAW it on paper (if you haven't, you should; I never cease to be amazed at how often people fail to do that, and helps explain how people get confused about numbers).

Draw a triangle rectangle (one of the sides is 0.9 AU long and you should imagine yourself watching from one of the triangle's corners). Imagine that the comet is spread along one of the triangle's sides; better yet, don't imagine it -- DRAW IT over the triangle's side. I think that when you see it it'll give you some idea of what to try next; but let us know if you're still stuck.

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There seems to be something wrong with, or rather missing from, this question. In the absence of some information about how the tail is oriented relative to the earth, it is impossible to answer.
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