A right triangle is a triangle in which one of the angles is a right angle, measuring exactly 90 degrees. This triangle is one of the most basic shapes in geometry and is fundamental in the study of trigonometry.
The sides of a right triangle are labeled relative to one of the angles other than the right angle. The side closest to this angle is referred to as the adjacent side, the side opposite the angle is referred to as the opposite side, and the hypotenuse is the side connecting the two.
Right triangles are essential in trigonometry because the ratio of the lengths of their sides defines the trigonometric functions sine, cosine, and tangent. Of course, it is worth mentioning that these functions are usually defined later in math using the unit circle which extends the definition to all angles and negative ratios.
An angle is a measure of rotation or turning and is usually measured in degrees or radians. In geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex. The size of an angle is determined by the amount of rotation from one ray to the other.
In math, the term "tangent" is used in both trigonometry and geometry. In trigonometry, tangent is one of the primary trigonometric functions. In geometry, a tangent refers to a straight line or plane that touches a curve at a single point without crossing through it at that point.