You're asking about the distance to a blue giant star, but you need to specify which one! There are many blue giant stars in the Milky Way galaxy and beyond.

To give you an accurate answer, I need to know which blue giant star you're interested in. For example, you could tell me:

* The name of the star: Is it Rigel (in Orion), Deneb (in Cygnus), or another star?

* Its location: Is it in a specific constellation or region of the sky?

Once you tell me which blue giant star you're thinking of, I can look up its distance from Earth.