# Finding length of isosceles triangle

I have the following homework question: find the length of side h. Assume the largest triangle is isosceles.

The way I'm thinking about it is that the 2 same angles could be any of the following options:

The answer is assuming that the 2 angles in Option A are the same, h=5.66.
I don't understand why Option B and Option C cannot be viable options? Why can't the 2 angles in either Option B or Option C be the same?

Thank you

Let the marked angle be $a$.
The other cases would imply $\frac{a}{2} + a + 90º = 180º$, or that $a = 60º$. This would mean that the triangle is equilateral. However, one of the sides is $2 + 2 = 4$, and one of the sides is $6$, so the triangle is not equilateral – a contradiction.