### Key Takeaways

- The Pythagorean theorem is crucial in various fields, including construction, manufacturing and navigation, enabling precise measurements and the creation of right angles for large structures.
- It underpins our entire system of measurement, allowing for accurate navigation by pilots and ships, and making GPS measurements possible through the calculation of distances and angles.
- Beyond navigation, the theorem is essential in geometry, physics, geology, engineering and even practical applications by carpenters and machinists.

OK, time for a pop quiz. You've got a right-angled triangle — that is, one where two of the sides come together to form a 90-degree angle. You know the length of those two sides. How do you figure out the length of the remaining side?

That's easy, provided that you took geometry in high school and know the Pythagorean theorem, a mathematical statement that's thousands of years old.

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The Pythagorean theorem states that with a right-angled triangle, the sum of the squares of the two sides that form the right angle is equal to the square of the third, longer side, which is called the hypotenuse. As a result, you can determine the length of the hypotenuse with the equation **a**^{2}** + b**^{2}** = c**^{2}, in which **a** and **b** represent the two sides of the right angle and **c** is the long side.

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