Geometry / trig problem

Question

If 10, 12 and x are sides of an acute angled triangle, how many integer vales of x are possible?

I came up with 13 for an answer. But I'm doubting my accuracy.

Answer 1

Unfortunately, only 9.

Let x is the largest side. The triangle will be acute if x² < 10² + 12²

x < √244 ≈ 15.62

Let x is not the largest side, the the largest side is 12. The triangle will be acute if 12² < 10² + x²

x > √44 ≈ 6.63

There are 9 possible integer values for x: 7, 8, .., 15.