Pythagoras’ Theorem

Pythagoras’ Theorem

  • Known as one of the core principles in geometry, Pythagoras’ theorem provides a method to calculate the length of one side in a right-angled triangle provided the lengths of the other two sides are known.

  • It is named after the ancient Greek mathematician Pythagoras, who essentially gave it a proof.

Formulation of Theorem

  • Pythagoras’ theorem can be written as: a² + b² = c².

  • In this equation, c represents the length of the hypotenuse (the side opposite the right angle), while a and b represent the lengths of the other two sides.

Practical Usages

  • The theorem finds real-life applications in a multitude of fields including architecture, construction, navigation, graphic design, and computer science among others.

  • In these sectors, Pythagoras’ theorem is utilised to determine distances, create accurate designs or figures, calculate areas, and navigate routes.

Solving Problems

  • To solve problems using Pythagoras’ theorem, first ensure that the triangle in question is a right-angled triangle.

  • If you have the lengths of a and b, substitute these values into the theorem to find c².

  • If you have the length of the hypotenuse (c) and one of the other lengths (a or b), rearrange the formula to solve for the unknown value.

  • Always remember to take the square root of your final answer when solving for a length.

Remember to revise these key concepts related to Pythagoras’ theorem and to continually practice problems associated with this principle to strengthen understanding and application skills.