Distance between 2 stars?

Question

Star "alpha" is 200 ly from Earth

Star "beta" is 150 ly from Earth

The angle between "alpha" and "beta" is 28 degrees

How far is "alpha" from "beta"

Answer 1

Well...

Is it okay if i don't answer the question but steer you a bit to help?

This is a standard geometry question.

Side Angle Side.  With this information you can solve the rest.

Use this as a reference, and good luck.

Answer 2

You need the Law of Cosines for a problem of this type, namely,

c^2 = a^2 + b^2 -2abcos(Gamma)

In this problem a = 200 ly, b = 150 ly, and Gamma = 28°.  We're looking for c.

c^2 = 200^2 + 150^2 - 2(200)(150)cos 28°

c^2 = 40,000 + 22,500 - 2 * 30,000 * 0.882947593

c^2 = 62,500 - 52976.85557 = 9523.144429

So c = 97.587 ly.