The sides of the triangle are AB = 4√5, BC = 4√2, AC = 10√2. What kind of triangle is it?

Determine the largest side of the triangle.
The largest side is the AC side = 10 * √2 cm.
Define the square of the length of the side of the speaker
AC ^ 2 = 100 * 2 = 200.
Determine the sum of the squares of the two remaining sides.
AB ^ 2 + BC ^ 2 = 16 * 5 + 16 * 2 = 112.
200> 112.
AC ^ 2> AB ^ 2 + BC ^ 2, hence the ABC triangle is obtuse.
Answer: The ABC triangle is obtuse.