If the sum of the squares of the lengths of the two shorter

If the sum of the squares of the lengths of the two shorter sides of a triangle is less than the square of the length of the longest side, what can you conjecture about the angle opposite the longest side? Explain. If the sum of the squares of the lengths of the two shorter sides of a triangle is greater than the square of the length of the longest side, what you can conjecture about the angle opposite the longest side? Explain.

Solution

Theorem- If the sum of the squares of the two shorter sides in a right triangle is greater than the square of the longest side, then the triangle is acute.

And the angle opposite to the longest side will be the acute angle that is angle less than 90 degree.

Theorem-If the sum of the squares of the two shorter sides in a right triangle is less than the square of the longest side, then the triangle is obtuse.

And angle opposite to largest side will be the obtuse angle that is angle greater than 90 degree and will be greatest of all three angles of a triangle.