The full Pythagoras formula is a² + b² = c².
This formula describes the relationship between the sides of a right-angled triangle. Let's break it down:
- a and b represent the lengths of the two shorter sides (legs or cathetus) of the right triangle. These sides form the right angle.
- c represents the length of the longest side, which is opposite the right angle. This side is called the hypotenuse.
The formula states that the sum of the squares of the lengths of the two shorter sides (a and b) is equal to the square of the length of the hypotenuse (c).
Example:
Imagine a right triangle where side a = 3 and side b = 4. To find the length of side c (the hypotenuse), we would use the formula:
3² + 4² = c²
9 + 16 = c²
25 = c²
To find 'c', we take the square root of both sides:
√25 = √c²
c = 5
Therefore, the length of the hypotenuse (c) is 5.
Applications:
The Pythagorean theorem has many applications in various fields, including:
- Construction: Ensuring buildings are square and stable.
- Navigation: Calculating distances and directions.
- Engineering: Designing structures and machines.
- Mathematics: Solving geometric problems.
In essence, the formula a² + b² = c² is a fundamental principle in geometry that links the side lengths of right triangles and has wide-ranging practical applications.
