Acute angle

Acute Angle

An acute angle is an angle that measures less than 90 degrees but more than 0 degrees. It is one of the basic concepts in geometry, a branch of mathematics.

Definition

In Euclidean geometry, an acute angle is defined as an angle formed by two rays or line segments that meet at a common point, known as the vertex, and open less than a right angle. The measure of an acute angle is always between 0 and 90 degrees, exclusive.

Properties

Acute angles have several important properties that distinguish them from other types of angles:

• All acute angles are positive.
• The sine, cosine, and tangent of an acute angle are all positive.
• In a right triangle, the two non-right angles are always acute.
• The complementary angle of an acute angle is an obtuse angle.

Applications

Acute angles are used in a variety of applications, including:

• In architecture and engineering, to design structures and machines.
• In navigation, to determine direction and distance.
• In trigonometry, to solve problems involving right triangles.

See also

• Obtuse angle
• Right angle
• Straight angle
• Reflex angle