Consider that a, b, c, are the length of sides of the triangle, where 'c' is the largest side.
Then according to Pythagorean Theorem, a triangle will be obtuse if
[tex]a^2+b^2Now, as per the given side measurements,[tex]a=\sqrt[]{5},\text{ b=4, c=5}[/tex]
Check is the condition satisfies,
[tex]a^2+b^2=(\sqrt[]{5})^2+(4)^2=5+16=21<5^2[/tex]
It is observed that the measurement values satify the necessary condition for obtuse triangle.
Therefore, the given triangle is an Obtuse Triangle.
