Need some help regarding phase and group velocity of a wave

Main Question or Discussion Point

I'm currently working with lasers and in relation to that, fiber optics. In the book I'm reading there's a section regarding modes and their "group velocity". The text claims that there is the following relation:
$$v_g=v_p * sin(A)$$
where $$v_g$$ is the group velocity and
where $$v_p$$ is the phase velocity and A is the incident angel as showed on the picture, although denoted as theta there.
From the picture you can see that the relation is reached by using trigonometry, and $$v_g$$ is in this case simply the velocity in the direction along the fiber. My question is, if this is the general idea of group velocity? I thought group velocity was the velocity of the "amplitude wave" in a wave packet? Am I wrong, or are there just different meanings of group velocity?

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Here is the picture!

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v_g found that way would be the velocity of the envelope of a wave packet.
It is the velocity of energy flow along the fiber direction.