Geometry

Question Analysis

This question focuses on applying the Pythagorean inequality theorems to classify a triangle. The main task is to determine if the triangle is acute, right, or obtuse by 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 . We know that , so .

Among , , and , the longest side . Let and .

2. Calculate and :

Calculate :

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