Question 255613
We have a thing called the triangle inverse theorem. This has three parts:
If {{{a^2 + b^2 < c^2}}} then triangle is obtuse
If {{{a^2 + b^2 = c^2}}} then triangle is right
If {{{a^2 + b^2 > c^2}}} then triangle is acute
We also have the triangle inequality statement which says
{{{a + b > c}}}
step 1 - apply our numbers to the inequality and we get
9+40 > 41. 
So, we have a triangle. Now we put the numbers into the inverse theorem and get
{{{9^2 + (40^2) __ 41^2}}}
{{{81 + 1600 __ 1681}}}
{{{1681 = 1681}}}
This is a right triangle.