Determine if the lengths of the sides of a triangle create a 'right, acute, or obtuse' triangle.

ANSWER
These three side lenghts form a right triangle
EXPLANATION
If the triangle is a right triangle, the side lenghts must satisfy the Pythagorean theorem. In a right triangle, the hypotenuse is always the longest side. Therefore, if it is a right triangle, the sum of the squares of the shorter sides must be equal to the square of the longest side:
[tex]\begin{gathered} 74^2=70^2+24^2 \\ 5476=4900+576 \\ 5476=5476 \end{gathered}[/tex]Therefore, this is a right triangle.