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
![a^2+b^2Now, as per the given side measurements,[tex]a=\sqrt[]{5},\text{ b=4, c=5}](https://img.qammunity.org/2023/formulas/mathematics/college/zq3rpqeif4rgyr1kn6bedvpzx757ca3yms.png)
Check is the condition satisfies,
![a^2+b^2=(\sqrt[]{5})^2+(4)^2=5+16=21<5^2](https://img.qammunity.org/2023/formulas/mathematics/college/ww58ygeu0i8t2s0uj0i9prf281cg1gxtbz.png)
It is observed that the measurement values satify the necessary condition for obtuse triangle.
Therefore, the given triangle is an Obtuse Triangle.