Geometry

Question Analysis

This question aims to classify a triangle as acute, right, or obtuse by using the Pythagorean inequality theorems. The main focus is on comparing the sum of the squares of the two shorter sides with the square of the longest side.

 

Key Concept Explanation

Pythagorean Theorem: For a right triangle with legs and and hypotenuse , .

Pythagorean Inequality Theorems:

If > , where is the longest side, the triangle is acute.

If < , where is the longest side, the triangle is obtuse.

 

Step - by - Step Solution

1. Identify the longest side:

First, estimate the value of . Among , , and , the longest side . Let and .

2. Calculate and :

Calculate :

.

Calculate :