Question

Explain the Pythagorean Theorem, its proofs and applications.

Answer 1

Answer:

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°.

I hope it's helpful for you ✌️

Answer 2

Answer:

The Pythagorean Theorem says

h^2 = a^2 + b^2

the hypotenuse squared = the sum of the squares of the two other sides of a right triangle,  the altitude squared + base squared.

It's a special case of the Law of Cosines

c^2 = a^2 + b^2 -2abCosC   where C= 90 degrees or pi/2,  

c^2 = a^2 +b^2 -2ab(Cos90)

c^2 =a^2 + b^2 -2ab(0)

c^2 = a^2 +b^2

There are 100+ proofs of the Theorem.  You can find them on line.

Mostly geometric in nature.  Former US President James A. Garfield invented a novel proof when he was in the House of Representatives.  His proof is published in math journals and can be found online.

The diagonal of a rectangle = d = the square root of the sum of the sides squared

d^2 = w^2 + l^2

d = square root of (w^2 + l^2)  where  w=width and l=length of the rectangle.

To know more about  Pythagorean Theorem refer :

https://brainly.com/question/14930619

https://brainly.com/question/29769496

#SPJ3