Why does the Pythagorean theorem work
More than 2,500 years ago, Pythagoras formulated a mathematical theory which is still used today. This theory states that the sum of the squares in a right triangle is equal to the square of the hypotenuse, or, in its more famous form, a2 + b2 = c2.
This works because of the distance between the hypotenuse of the triangle is directly equal to the two square on the outside. In reality, there are many applications for the Pythagorean Theorem. One of the most useful applications of the theorem is using it to find the distance between two cities. When it comes to using the Pythagorean theorem, there are a few things to keep in mind in order to use it properly. As you set up the equation, it can help to draw a diagram of what you’re trying to find the distance between. This helps you keep it on scale, in addition to finding the information you need to make the equation work. The first thing to remember about the Pythagorean Theorem is that the hypotenuse is always across from the right angle and it does not touch or intersect the right angle in any way. It is also the longest side of the right triangle, and it is always labeled as ‘c’ in the famous equation.
If after you complete your diagram, you discover that what you have is not a right triangle, you’ll not be able to use Pythagoras’ Theorem, since it can only be used on right triangles. Instead, you’ll have to use the Law of Sines or Cosines to find your value instead. In addition, you’ll need to have at least two side measurements in order to figure out the remaining measurement. You cannot complete the Pythagorean Theorem with only one side measure, as the two sides must be squared and added together to find the remaining side information. If you find that you only have one side measurement, you’ll have to use the 30-60-90 rules of trigonometry in order to find the other side information before you can use the Pythagorean Theorem.
While its impossible to use the Pythagorean theorem on anything but a right triangle, it is possible to use other theorems and corollaries available to better understand different types of triangles. These theories and corollaries combined with the Pythagorean Theorem will allow you to find the distance between any two objects.