Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: $$c^2 = a^2 + b^2$$ .

The Pythagorean Theorem ONLY works on right triangles.

You can use the Pythagorean Theorem. If the ladder is the hypotenuse (c) and the height it reaches on the wall is one side (a), then the distance from the wall (b) can be found using: $$b = \text{sqrt}(c^2 - a^2)$$ .

A Pythagorean Triple consists of three positive integers (a, b, c) that satisfy the equation $$a^2 + b^2 = c^2$$ . For example, (3, 4, 5) is a Pythagorean Triple.

Using the Pythagorean Theorem: $$d = \text{sqrt}(13^2 + 16^2) = 5\text{sqrt}(17) m$$ .

The formula to find the hypotenuse (c) is: $$c = \text{sqrt}(a^2 + b^2)$$ .

Using the Pythagorean Theorem: $$c = \text{sqrt}(5^2 + 12^2) = 13$$ .

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, expressed as $$c^2 = a^2 + b^2$$ .

The simplified form is $$15ab^3c^2\text{sqrt}(5ac)$$ .

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.