# Using Tully Fisher to measure Distance Problem

Can anyone explain by looking at the solution in the pic, how did the cos (i) came about? I guess they are getting this from the major-minor axis info in the question, but I am not sure about the derivation.

Also v=300/sin(i), what is this formula?

Many thanks :)

• I think it is just an assumption on the inclination of the plane of the galaxy with respect to the line of sight of the observer. – Py-ser Sep 24 '14 at 5:28
• you were correct! its about inclination. The answer by Aaron has attached notes (if you are curious) :) – Hari Sheldon Sep 24 '14 at 23:39
• Yeah, but as @Aaron showed, it was not just "an assumption", you can derive it from the major-minor axis ratio. It was weird, indeed, that that parameter was not used in the solution... – Py-ser Sep 25 '14 at 1:50

With the Tully Fisher relation, the inclination angle is determined from the major-minor axis ratio where $sin(i) = \sqrt{1-q^2}$ and q is the inverse of your ratio.

You need to apply the sine of the angle to the rotational velocity because the measure is based on our line of sight observation which must be converted to the true 3D velocity.

• Thank you Aaron! This was indeed helpful especially the detailed attached notes! T-F is looking less mysterious slowly but surely :) – Hari Sheldon Sep 24 '14 at 23:37