In a triangle, which angle is opposite the longest side?

In any triangle, the relationship between the lengths of the sides and the measures of the angles is defined by a fundamental property: the longest side is always opposite the largest angle. This means that if you have a triangle with one side that is longer than the other sides, the angle opposite that longest side must be the largest angle in the triangle. This relationship holds true regardless of the type of triangle, whether it is acute, right, or obtuse.

The reason for this relationship can be understood through the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Consequently, to maintain this balance, a larger side necessitates a larger angle opposite it.

Therefore, identifying that the angle opposite the longest side of a triangle is the largest angle aligns perfectly with this principle of geometry, confirming that the correct answer is indeed the largest angle.