Question

The three sides of AJKL

measure 11.2 feet, 21 feet, and
23.8 feet. IS AJKL an acute,
right, or obtuse triangle?

Answer 1

right triangle

Explanation:

I find it convenient to answer questions like this by computing a "form factor" that subtracts the square of the long side from the sum of the squares of the shorter sides. The sign of this value is the sign of the cosine of the largest angle in the triangle.

f = a² +b² -c²

f = 11.2² +21² -23.8²

f = 125.44 +441 -566.44 = 0

The cosine of the largest angle is 0, so that angle is 90° and the triangle is a right triangle.