The Pythagorean Theorem is so elegant and practical that it is still used today.The sum of the squares of non- hypotenuse sides is equal to the square in the right triangle.The Pythagorean Theorem is a fundamental pillar of basic geometry and has countless practical applications.

Step 1: Make sure your triangle is a right triangle.

The definition of a right triangle is only applicable to the Pythagorean Theorem.To be a right triangle, you have to have one angle of 90 degrees.Right angles are marked with a small square, rather than a rounded curve, as a form of visual shorthand.There is a mark in one of the corners of your triangle.

Step 2: The sides of your triangle should be assigned the variables a, b, and c.

In the Pythagorean Theorem, the sides that meet in a right angle are referred to by the variables a and b, while the hypotenuse is always opposite.It doesn't matter which side is labeled 'a' or 'b', you should assign the variables a and b to the shorter sides of the triangle.

Step 3: Determine which side of the triangle is being solved for.

The Pythagorean Theorem allows mathematicians to find the length of a right triangle if they know the lengths of the other two sides.If only one of your sides has an unknown length, you're ready to go.We know that our hypotenuse is 5 and one of the other sides is 3, but we don't know what the third side is.Because we know the lengths of the other two sides, we're ready to go!This example problem will be returned in the following steps.To use the Pythagorean Theorem, you need to know the length of one side.If you know one of the non-right angles in the triangle, you can use basic trigonometry functions.

Step 4: Put your two values into the equation.

The sides of the triangle are non hypotenuse.We know the length of one side and the hypotenuse, so we would write our equation as such.

Step 5: You have to calculate the squares.

Take the square of your known sides to solve the equation.If you find it easier, you can square your side lengths later.In our example, we would get 3 and 5.We can change our equation to 9 + b2 + 25.

Step 6: On the other side of the equals sign, put your unknown variable.

To get your unknown variable on one side of the equals sign and two squares on the other side, use basic algebra operations.If you're solving for the hypotenuse, you won't need to isolated it.Our current equation is 9 + b2Let's take 9 from both sides of the equation.This leaves us with 16.

Step 7: The sides of the equation have a square root.

You should have one variable squared on one side of the equation and a number on the other side.To find the length of your unknown side, take the square root of both sides.Taking the square root of both sides gives us b.The unknown side of the triangle is what we can say is length.

Step 8: The sides of real-world right triangles can be found using the Pythagorean Theorem.

The Pythagorean Theorem is applicable in a lot of practical situations.You can use the Pythagorean Theorem to find the length of one of the sides if you know how to recognize right triangles in real life.It's a little more difficult to do a real-world example.A ladder is leaning.There is a ladder at the bottom of the wall.The ladder goes up the wall of the building.What is the length of the ladder?We can see the lengths of the sides of our triangle by looking at "5 meters from the bottom of wall" and "20 meters up the wall".We can think of this arrangement as a right triangle with the ladder leaning against the wall and the ground next to it.The hypotenuse of the ladder is unknown.The Pythagorean Theorem states that a2 + b2 is the same as a5 + (20)2 and a25 + 400.The ladder has an approximate length.

Step 9: There are two points in the X-Y plane.

The straight-line distance between two points in the X-Y plane can be calculated using the Pythagorean Theorem.The x and y coordinates of any two points are all you need to know.The coordinates are usually written as ordered pairs.To find the distance between the two points, we will use the non-right angle corners of a right triangle.The hypotenuse is the distance between the two points if you find the length of the a and b sides.

Step 10: There are two points on a graph.

In an X-Y plane, the coordinate on the horizontal axis and the vertical axis is given by x and y, respectively.You can find the distance between the two points without a graph, but you have to use a visual reference to make sense of it.

Step 11: The lengths of the non-hypotenuse sides of your triangle can be found.

Use your two points as the corners of the triangle next to the hypotenuse to find the lengths.If you want to do this visually, you can use the formulas x1 - x2 for the horizontal side and y 1 - y2 on the vertical side.Let's say we have two points.The side length of the horizontal side is: x1 - x2

Step 12: The Pythagorean Theorem can be used to solve the hypotenuse.

The hypotenuse of the triangle's two sides is the distance between your two points.If you want to find the hypotenuse, use the Pythagorean Theorem to set the length of your first side and the second side.Our side lengths are 3 and 4 so we would find the hypotenuse in this example.The distance is between 3 and 6.