Question

Analyze the diagram below and complete the instructions that follow.

Use Pythagorean inequalities to classify the triangle above.

A. acute
B. obtuse
C. right
D. both acute and right

Answer 1

Let "a", "b" and "с" be sides of the triangle ("с" is the longest side). The triangle will be:
right if a² + b² = c²
аcute if a² + b² > c²
obtuse if a² + b² < c²

We have a=32.18, b=40 and c=53.02

a² + b² = 32.18² + 40² = 1035.5524 + 1600 = 2635.5524
and
c² = 53.02² = 2811.1204

2635.5524 < 2811.1204 ⇒ obtuse triangle