A triangle is a three-sided polygon where the sum of its interior angles equals 180 degrees. Some common formulas for triangles include perimeter, the total sum of its individual side lengths; area, one-half of the product of a triangle’s base and height; and angle calculations based on the Pythagorean Theorem.

The Pythagorean Theorem states that the side lengths of a right triangle follow the pattern a squared + b squared = c squared, where a and b represent the triangle’s two shorter sides and c represents the triangle’s hypotenuse.

From this relationship, a set of trigonometric functions emerges to describe the geometric connections among the triangle's side lengths and interior angles. Commonly known as SOHCAHTOA, these relationships are: sine (angle) = opposite/hypotenuse; cosine (angle) = adjacent/hypotenuse; and tangent (angle) = opposite/adjacent.