The land of Pythagoras' Theorem

The land of Pythagoras' Theorem will have you seeing square roots but if you remember the formula your sure to make it from a squared to b squared and final destination c squared.

Pythagoras' Theorem

Years ago, a man named Pythagoras found an amazing fact about triangles: If the triangle had a right angle (90°) ... ... and you made a square on each of the three sides, then ... ... the biggest square had the exact same area as the other two squares put together! The Pythagorean Theorem itself The theorem is named for a Greek mathematician named Pythagoras. He came up with the theory that helped to produce this formula. The formula is very useful in solving all sorts of problems. The Pythagorean Theorem helps us to figure out the length of the sides of a right triangle. If a triangle has a right angle (also called a 90 degree angle) then the following formula remains true: a2 + b2 = c2 Note: c is the longest side of the triangle a and b are the other two sides Where a, b, and c are the lengths of the sides of the triangle (see the picture) and c is the side opposite the right angle. The longest side of the triangle is called the "hypotenuse", so the formal definition is: In a right angled triangle: the square of the hypotenuse is equal to the sum of the squares of the other two sides. Let's work through a few examples: 1) Solve for c in the triangle below: In this example a = 3 and b=4. Let's plug those into the Pythagorean Formula. a2 + b2 = c2 32 + 42 = c2 3x3 + 4x4 = c2 9+16 = c2 25 = c x c c = 5 2) Solve for a in the triangle below: In this example b=12 and c= 15 a2 + b2 = c2 a2 + 122 = 152 a2 + 144 = 225 Subtract 144 from each side to get: 144 - 144 + a2 = 225 - 144 a2 = 225 - 144 a2 = 81 a = 9 Picks Theorem Area(P) = i + (b/2) - 1