The Pythagorean Theorem is a mathematical principle that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The Pythagorean Theorem can be proven using various methods, including algebraic, geometric, and trigonometric proofs. One of the most commonly used proofs involves using the relationships between sine, cosine, and the sides of a right triangle.
In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, while the cosine of an angle is equal to the length of the side adjacent to the angle divided by the length of the hypotenuse. This relationship can be used to prove the Pythagorean Theorem.
No, the Pythagorean Theorem can only be applied to right triangles. In non-right triangles, the Law of Cosines and Law of Sines are used to find missing side lengths or angles.
The Pythagorean Theorem has many real-life applications, such as in construction and engineering for calculating distances and angles. It is also used in navigation, astronomy, and other fields that involve measuring distances and angles.