The role of a Pythagorean calculator is to calculate the length of a hypotenuse or missing leg of a right-angled triangle. The hypotenuse sits opposite the right angle of the triangle, and you can identify this side using a hypotenuse formula. The hypotenuse formula also goes hand-in-hand with the Pythagorean Theorem.

When you are using a Pythagorean calculator, it’s helpful to know that a right triangle has a 90-degree angle and the two remaining angles total 90 degrees as well. The sum of all angles in a triangle is 180 degrees. Below, you can learn all about the Pythagorean Theorem and how to use it.

What is the Pythagorean Theorem?

The Pythagorean Theorem involves a right triangle and its three sides. It relates to Euclidean geometry. The squares of the hypotenuse equal the squares of the right triangle’s sides. The Pythagorean Theorem is also the hypotenuse formula, which is as follows:

a² + b² = c²

The theorem gets its name from ancient mathematician and philosopher Pythagoras, but nothing in history suggests he ever used or worked on this theorem himself.

The Pythagorean Theorem and How to Use it

1.	Establish the hypotenuse (triangle’s legs) and put them into the formula. For this example, you know that angle A is 10 and B is 5. 

   2.	The formula now reads:
10² + 5² = C²

   3.	Square the length values to get the final figure.
100 + 25 = C²
125 = C²
   4.	Get the square root of both equations to get the figure of C which is: 
C = 11.18

If you are trying to establish the value of A or B, you will need to isolate the variable before you take the square root and combine the other values. 

This Pythagorean calculator will take care of all the hard work for you. However, if you prefer to know how to get the answer on your own, you can use this above formula.

What is the Hypotenuse Formula?

You may hear the hypotenuse formula and Pythagorean formula used interchangeably, but there are a few differences. The hypotenuse formula uses the Pythagorean formula to solve the hypotenuse (C).  Take the square root of both equations to solve (C). 

The answer would look like this:
c = √ (a² + b²).

Things to Consider When Solving Problems with Triangles

Sometimes, triangles within problems you are solving have a slope or gradient to trip you up. In problems with right triangles, the right-angled parts will have a -1 product. You can use the following formula to determine the degree of the slope. 

(y₂ - y₁) / (x₂ - x₁)

For this example, we determine that the coordinates are (2,4) and (5,10), with the segment’s slope being (10-4) / (5-2) = 1.

If the slope forms the -1 angle, the lines would be perpendicular. After all, 1 x -1 = -1. You can determine, then, that the triangle is a right triangle. You can also use a slope formula calculator to work out the problem quickly.

If you find that any angles in the triangle are given as degrees, you can convert them to radians effortlessly. Identify the angle and multiply it by 180 / π. If it’s in radians, multiply it by π / 180.