Question

the sides of a triangle are 54,31,and 69. use the phone ythagorean theorem to determine if the triangle is right acute or obtuse.

Answer 1

Answer:

obtuse

Step-by-step explanation:

a² + b² = c²

Let's use the two shorter sides as legs.

a² + b² = 31² + 54² = 961 + 2916 = 3877

c = √3877 = 62.2655...

For the triangle to be a right triangle, the third side would have to have a length of 62.2655. The actual length of the third side is 69. 69 is greater than 62.3, so the angle between the sides 31 and 54 must be greater than 90°. Therefore the triangle is an obtuse triangle.