An acute triangle is a type of triangle where all three of its interior angles are less than 90 degrees. This classification sets it apart from obtuse triangles, which have one angle greater than 90 degrees, and right triangles, which have one 90-degree angle. Acute triangles are notable for their sharp, narrow angles.
Key Properties of Acute Triangles
- All angles are less than 90 degrees: The defining characteristic of an acute triangle is that each of its angles is acute.
- Can vary in side lengths: Acute triangles can be equilateral (all sides equal), isosceles (two sides equal), or scalene (no sides equal).
- Angles are directly related to the sides: In an acute triangle, the longest side is opposite the largest acute angle, and the shortest side is opposite the smallest acute angle.
Examples of Acute Triangles
Example 1: A triangle with angles of 30 degrees, 60 degrees, and 90 degrees is an acute triangle, as all angles are less than 90 degrees.
Example 2: An equilateral triangle with each angle measuring 60 degrees is also an acute triangle.
Significance of Acute Triangles
Acute triangles are frequently encountered in geometry, especially in studies related to triangle congruence, similarity, and trigonometry. They are also common in various architectural and engineering designs due to their balanced and symmetrical properties.
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