How do you explain the Pythagorean Theorem?

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

Why is the cosine rule a Generalisation of Pythagoras?

a2 = b2 + c2 – 2bc cos 90º. a2 = b2 + c2 – 2bc cos 90º = b2 + c2 – 2bc × 0 = b2 + c2. And this gives us exactly what Pythagoras’ Theorem gives us because a is the side opposite the right angle – it is the hypotenuse of the triangle. So the Cosine Rule is a generalisation of Pythagoras’ Theorem.

Did Pythagoras prove his theorem?

Pythagoras is immortally linked to the discovery and proof of a theorem, which bears his name – even though there is no evidence of his discovering and/or proving the theorem. Greek mathematician Euclid, referred to as the Father of Geometry, lived during the period of time about 300 BCE, when he was most active.

How the Pythagorean Theorem can be used in the real world?

Real Life Application of the Pythagoras Theorem The Pythagorean Theorem is useful for two-dimensional navigation. You can use it and two lengths to find the shortest distance. … Painting on a Wall: Painters use ladders to paint on high buildings and often use the help of Pythagoras’ theorem to complete their work.

How does cosine rule work?

The cosine rule, also known as the law of cosines, relates all 3 sides of a triangle with an angle of a triangle. Similarly, if two sides and the angle between them is known, the cosine rule allows one to find the third side length.

How the Pythagorean theorem can be used in the real world?

What is the conclusion of Pythagoras theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

What is Pythagorean Theorem used for in real life?

Architecture and Construction Given two straight lines, the Pythagorean Theorem allows you to calculate the length of the diagonal connecting them. This application is frequently used in architecture, woodworking, or other physical construction projects.