Discovering The Obtuse Triangle Inequality And Its Role In Identifying Obtuse Triangles

Regarding side length, a triangle is an obtuse triangle if …

a² + b² < c²

A triangle is considered obtuse if one of its angles measures greater than 90 degrees. Specifically, if the square of the longest side is greater than the sum of the squares of the other two sides in the triangle, then the angle opposite the longest side will be obtuse. This is known as the obtuse triangle inequality. For example, if a triangle has side lengths of 7, 8, and 10, then it is an obtuse triangle because 10^2 is greater than (7^2 + 8^2).

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