How do you find if this is a right, obtuse, or acute triangle?

It should be a right triangle as u can use phytgagrean theorem to figure it out basically a^2+b^2 = c^2 this works in this case as it should equal to 10^2 + 5 square root 2 and then Ans squared = 5 square root 6 then squared . At end it should equal to 150= 150