Right Angle Triangles are used frequently in physics to allow the physicist a simple means of working with vector quantities. Geometry gives us the Pythagorean Theorem and Trigonometry gives us the Sine, Cosine, and Tangent functions to work with both the angles and the lengths of sides in right angle triangles.

1. Pythagorean Theorem: This Theorem which date back to the Greeks, provides us with a relationship among the three sides of a right angle triangle. What this theorem says is that the square of the longest side, opposite the right angle, is equal to the sume of the squares of the other two sides. Consider the following example.

Example:
 
 

The Theorem of Pythagorus

2. Sine, Cosine, and Tangent Functions: These three trigonometric functions are commonly used in physics. They relate to right angle triangles, and are frequently used to solve for unknown angles and unknown lengths of sides.

The Sine function: The sine function is defined as the ratio of the length of the side opposite one of the non-right angles to the length of the hypotenuse. This function is written as:
 
 

The Cosine function: The cosine function is defined as the ratio of the length of the side adjacent to one of the non-right angles to the length of the hypotenuse. This function is written as:
 
 

The Tangent function: The tangent function is defined as the ratio of the length of the side opposite one of the non-right angles to the length of the side adjacent to the same angle. This function is written as:
 
 
 

Note that these realationships between ratios of sides and these function values of Sine, Cosine, and Tangent are the same regardless of whether the triangle is small or large. See the example below:
 
 

Trig Function Ratios