Understanding Acute Angles: Definition, Examples, and Importance in Mathematics

Acute Angle

Any angle smaller than 90 degrees (1° to 89°)

An acute angle is a type of angle that measures less than 90 degrees. In other words, if you were to visualize an acute angle, it would appear smaller than a right angle (90 degrees) and larger than a straight angle (180 degrees). The word “acute” in mathematics is derived from the Latin word “acutus,” which means “sharp.”

To understand this concept visually, imagine drawing a line segment and then extending two other line segments from the endpoints of the original segment. The point where these two new segments meet forms an angle. If the measure of this angle is less than 90 degrees, it is considered an acute angle.

You can also encounter acute angles in everyday life. For example, when you fold a sheet of paper to make a triangular shape, the angles formed at the corners of the triangle are acute angles. Additionally, the acute angles of a right triangle play a crucial role in trigonometry, where they are used to define ratios such as sine, cosine, and tangent.

It is important to distinguish between acute angles and obtuse angles. While an acute angle measures less than 90 degrees, an obtuse angle measures more than 90 degrees but less than 180 degrees. So, acute angles are smaller and “sharper” than a right angle, whereas obtuse angles are larger and more “open” than a right angle.

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