Pythagorean Theorem Overview

Introduction to the Pythagorean Theorem

• The Pythagorean theorem is a fundamental principle in mathematics used to relate the sides of a right triangle.

• The theorem can be stated as follows:

  • Formula: a^2 + b^2 = c^2

  • Where:

    • a and b are the lengths of the legs of the right triangle.

    • c is the length of the hypotenuse (the side opposite the right angle).

Application of the Pythagorean Theorem

• In practical terms, to solve a problem involving the Pythagorean theorem, one must identify the lengths of the two legs.

• Example Problem: Calculate the hypotenuse where one leg is 20 units and the other leg is 25 units:

  • Given:

  • a = 20

  • b = 25

  • Substitute into the formula:

  • 20^2 + 25^2 = c^2

  • Calculate the squares:

  • 20^2 = 400

  • 25^2 = 625

  • Combine the results:

  • 400 + 625 = c^2

  • 1025 = c^2

  • To find c (the length of the hypotenuse), take the square root:

  • c = \sqrt{1025}

  • This simplifies roughly to:

    • c \approx 32.015 (rounded to three decimal places)

Conclusion

• The Pythagorean theorem provides a crucial tool for calculating the relationship between the sides of right triangles, applicable in numerous fields such as architecture, engineering, and various branches of science.