Pythagorean Theorem

Trigonometry is the analysis of the unique geometric properties of a right triangle using the Pythagorean Theorem. It was known in ancient times by the Babylonians and was described in a theory by the ancient Greek mathematician Pythagoras. The trigonometric functions and the trigonometric laws are all based on the proof of the Pythagorean Theorem. The theorem states that if a right triangle has two sides equal to a and b, and a hypotenuse equal to c, then a squared plus b squared equals c squared. The hypotenuse of a right triangle is the side opposite the right angle. There are six trigonometric functions the sine, the cosine, the tangent, the cosecant, the secant and the cotangent that examine the ratios of two sides of a right triangles. The last three are reciprocals of the first three. To determine that this is true for any right triangle means mathematically proving the Pythagorean theorem using basic geometry. This mathematical relationship regarding the geometry of right triangles produces a method for solving a triangle.

Pythagorean Theorem:
In any right triangle with sides a and b and hypotenuse c,
then a² + b² = c²
or c is equal to the square root of the quantity a squared plus b squared.

Pythagorean Theorem Example:
If a right triangle has sides a = 3 and b = 4 and hypotenuse c = 5,
then 3² + 4² = 5², and 9 + 16 = 25.