Question

Using the side lengths, determine whether the
triangle is acute, obtuse, or right.

Answer 1

Explanation:

In an acute triangle, the size of all the angles are less than 90 degrees. In a right triangle, the size of one angle which is also the largest is 90 degrees. In an obtuse triangle, the size of the largest angle is greater than 90 degrees but lesser than 180 degrees. Looking at the given triangle,

1) it is not obtuse because are the angles are smaller than 90 degrees

2) it is not right angle because Pythagorean theorem does not hold. It means

61² + 11² ≠ 91²

3842 ≠ 8281

Since the size of all the angles are below 90 degrees, then it is an acute triangle.