# How To Solve Pythagorean Theorem Problems

Because of these angles it´s easier to find out the sides of a right triangle.Let´s try to understand this by using two examples.Pythagoras or the disciples to him constructed the first known algebraic proof of the theorem and famous writers such as Plutarch and Ciceron acclaimed him for discovering this proof.

Among these, the Primitive Pythagorean Triples, those in which the three numbers have no common divisor, are most interesting.

A few of them are: Also Pythagorean Triples can be created with the a Pythagorean triple by multiplying the lengths by any integer. We see looks like the legs of a right triangle with a multiplication factor of 111.

A Pythagorean Triple is a set of 3 positive integers such that , i.e.

the 3 numbers can be the lengths of the sides of a right triangle.

For example, Right triangle has legs of length and .

One of the most used and beautiful theorems in math is the Pythagorean theorem.Lets call the hypotenuse $c$ which gives us that $c^2=1^2 1^2$ $c^2=2$ Take the square root $c=\sqrt ≈ 1,414$ There exists a couple of special types (or cases) of right triangles.Two of them being $30°-60°$ right triangles and °-45°$right triangles.This theorem has been know since antiquity and is a classic to prove; hundreds of proofs have been published and many can be demonstrated entirely visually(the book The Pythagorean Proposition alone consists of more than 370).The Pythagorean Theorem is one of the most frequently used theorems in geometry, and is one of the many tools in a good geometer's arsenal.In this type of triangle the opposite side of the °$ angle is half of the hypotenuse: $b=\frac12 ·c = 0,5·c$ In a 45-45 degree right triangle we can get the length of the hypotenuse by multiplying the length of one leg by $\sqrt$ to get the length of the hypotenuse: $c = \sqrt·a = \sqrt·b$ In this section you will find examples and solutions where we use the pythagorean theorem to solve these problems, even if they aren´t directly connected to a right triangle. : The blue point has the coordinates (1, 1) and the red point has the coordinates (5, 3).Now let´s draw lines to form a right triangle where we use the two points as corners.1 Understanding the Pythagorean theorem 1.1 The theorem 1.2 A brief history 2 Basic examples where Pythagoras theorem is used 2.1 Find the length of the hypotenuse in a right triangle 2.2 Find the length of a leg in a right triangle 2.3 Is it a right triangle? 2.5 Special types of right triangles, 30°-60° and 45°-45° right triangles 3 More advanced examples 3.1 Distance between two points 3.2 The distance formula 3.3 The diagonal distance in a cube 4 Continue to learn more about the Pythagorean theorem The Pythagorean theorem or Pythagoras’ theorem is a relationship between the sides in a right triangle.A right triangle is a triangle where one of the three angles is an 90-degree angle.Let´s call the hypotenuse $c$ and calculate the distance.$c^2=4^2 2^2$ $c^2=16 4$ $c^2=20$ $c=\sqrt ≈ 4,47$ This format will always hold true and because of that we can form a formula called the distance formula.

## Comments How To Solve Pythagorean Theorem Problems

• ###### Learn Pythagorean Theorem Problems Solving Right Triangles

Pythagorean Theorem Examples Solving Right Triangle Problems. Pythagorean theorem problems start by giving you the length of two of the sides of a right triangle. Using the Pythagorean formula, it is possible to calculate the length of the third side. Because you are using squares and square roots, you may need the help of a calculator.…

• ###### Ways to Solve Pythagoras Theorem Questions - wikiHow

When doing word problems about traveling, if you are meant to find the shortest distance you will likely use the Pythagorean Theorem. The shortest distance will be the length of the hypotenuse of a triangle superimposed over the area. Learn the most common Pythagorean triples by heart.…

• ###### Pythagorean theorem word problems - Basic mathematics

Pythagorean theorem word problems. Let the length of the ladder represents the length of the hypotenuse or c = 13 and a = 5 the distance from the ladder to the wall. The ladder will never reach the top since it will only reach 12 feet high from the ground yet the top is 14 feet high.…

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• ###### Solving Problems Involving the Pythagorean Theorem

Draw a right triangle and then read through the problems again to determine the length of the legs and the hypotenuse. Step 2 Use the Pythagorean Theorem a 2 + b 2 = c 2 to write an equation to be solved. Remember that a and b are the legs and c is the hypotenuse the longest side or the side opposite the 90º angle.…

• ###### Pythagorean Theorem calculator - Basic mathematics

Pythagorean Theorem calculator. The Pythagorean Theorem calculator will help you to solve Pythagorean problems with ease. Note that the triangle below is only a representation of a triangle. Your triangle may have a different shape, but it has to be a right triangle. If you looking for either a or b, make sure that the value you enter for a or b is not bigger or equal to c.…

• ###### How to Use the Pythagorean Theorem. Step By Step Examples and Practice

Use the Pythagorean theorem to calculate the value of X. Round your answer to the nearest hundredth. Remember our steps for how to use this theorem. This problems is like example 2 because we are solving for one of the legs.…