Can someone please explain the Pythagorean Theorem to me?! I seriously don't get it.
The Pythagorean Theorem is: for example
(hypotenuse) squared = (leg) squared + (leg) squared
14 squared =7 squared +x squared
196=49+x squared
147=x squared
the square root of 147=x squared
the square root of 49 times the square root of 3=x
7 the square root of 3=x
a^2 + b^2 = c^2
c = hypotenuse of a right angle triangle
a = one side of a right angle triangle
b = one side of a right angle triangle
So -- we square each side and add them together. The sum is the square of the hypotenuse.
Example:
4^2 + 6^2 = c^2
16 + 36 = 52
The square root of 52 = 7.211
The hypotenuse is 7.211
Study this site carefully.
http://www.mathsisfun.com/pythagoras.html
Thank you!
Of course! I'd be happy to explain the Pythagorean Theorem to you.
The Pythagorean Theorem is a fundamental principle in mathematics that relates to right triangles, which are triangles that have one angle measuring 90 degrees (a right angle). It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In mathematical terms, the Pythagorean Theorem can be expressed as:
c^2 = a^2 + b^2
Where:
- c represents the length of the hypotenuse
- a and b represent the lengths of the other two sides, often called the "legs" of the triangle.
To better understand the theorem, let's walk through an example. Suppose you have a right triangle with side lengths of 3 units and 4 units. To find the length of the hypotenuse, you can use the Pythagorean Theorem:
c^2 = a^2 + b^2
c^2 = 3^2 + 4^2
c^2 = 9 + 16
c^2 = 25
To solve for c, you take the square root of both sides of the equation:
c = √25
c = 5
So, in this example, the length of the hypotenuse is 5 units.
To apply the Pythagorean Theorem, you need to know the lengths of two sides of the right triangle. Once you have those lengths, you can substitute them into the theorem and solve for the unknown side. This theorem is commonly used in geometry and has many practical applications, such as calculating distances or determining the length of one side of a triangle given the lengths of the other two sides.