If the largest angle of a triangle is 120° and it is included between sides of 1.5 and 0.5, then to the nearest 10th the largest side of the triangle is what?

Just apply the cosine law:
Let AB, be the side opposed to the angle 120°

AB² = (05)² +(1.5)² -2(0.5)(1.5).cos(120°). But we know that cos(120°) = -1/2
Then:

AB² = 0.25 + 2.25 + 0.75
AB² = 3.25

And AB =√3.25 = 1.8