Understanding the Pythagorean Theorem | Explained, Examples, and Applications

a^2+b^2=c^2

The equation a^2 + b^2 = c^2 represents the Pythagorean theorem, which is one of the fundamental concepts in geometry

The equation a^2 + b^2 = c^2 represents the Pythagorean theorem, which is one of the fundamental concepts in geometry. It relates the lengths of the sides of a right triangle, where a and b are the lengths of the two shorter sides, often called the legs, and c is the length of the longest side, which is also known as the hypotenuse.

The Pythagorean theorem states that in any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. In other words, if you square the lengths of the two legs and add them together, it will be equal to the square of the length of the hypotenuse.

This theorem is useful in many practical applications, such as determining the lengths of sides in real-world right triangles or solving problems involving distance, for example in navigation or construction.

For example, let’s say we have a right triangle with sides of lengths a = 3 and b = 4. We can use the Pythagorean theorem to find the length of the hypotenuse, c.

a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2

Taking the square root of both sides, we find that c = 5. Therefore, the length of the hypotenuse is 5 units.

The Pythagorean theorem is not limited to specific values of a, b, and c. It holds true for all right triangles, regardless of the lengths of their sides, as long as it satisfies the condition of being a right triangle.

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