An acute triangle is a type of triangle where all three of its interior angles are acute, meaning each angle measures less than 90 degrees. In other words, in an acute triangle, none of the angles is a right angle (90 degrees) or an obtuse angle (greater than 90 degrees). The sum of the three interior angles in any triangle is always 180 degrees.

Characteristics of an acute triangle:-

  1. Interior Angles: All three interior angles are less than 90 degrees.
  2. Sum of Angles: The sum of the three interior angles is exactly 180 degrees.
  3. Shape: It has a sharp or pointed appearance.

The opposite classification to an acute triangle is an obtuse triangle, where at least one of the interior angles measures more than 90 degrees. In contrast, a right triangle has one angle exactly equal to 90 degrees.

In an acute triangle, the sides opposite the acute angles are shorter in comparison to the side opposite the largest angle (which is less than 90 degrees). Additionally, the altitude from any vertex of an acute triangle falls within the triangle, intersecting the opposite side.

Here's an illustration of an acute triangle:-


In the above triangle ABC:

  • Angle A, Angle B, and Angle C are all acute angles (each less than 90 degrees).

Acute triangles have applications in various fields, and their properties are used in geometry, trigonometry, and other mathematical and scientific disciplines.