Pythagorean Theorem Calculator
If you find it hard to solve problems related to right-angle triangles, then you can use our Pythagorean Theorem Calculator. It uses the theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the number we get from adding the squares of the other two sides.
To use the calculator, simply input the lengths of two sides of the triangle. The calculator will then compute the length of the hypotenuse, or alternatively. It calculates the size of one side if you know the hypotenuse and the other side.
a^{2} +b^{2} =c^{2}
c = a^{2} + b^{2}
This tool is best suited for students, educators, and professionals who have geometric problems. It provides quick and accurate results.
Hypotenuse Length:
What is Pythagorean Theorem?
A Pythagorean Theorem is the theorem that is used to calculate the length of the third side of a right-angle triangle if we know the length of the other two sides. The definition is: The length of the hypotenuse of a right-angle triangle is equal to the total of squares of the other two sides of it.
The formula is expressed as a2 +b2 =c2, where ‘c’ represents the hypotenuse, and ‘a’ and ‘b’ are the other two sides.
Component | Description | Formula |
Side A | A perpendicular side of the triangle(out of two) | Given or calculated value |
Side B | The other perpendicular side of the triangle | Given or calculated value |
Hypotenuse | The side opposite the right angle | a2 +b2 |
Hypotenuse Calculation | How to determine the hypotenuse using the formula | side A2 + side B2 |
How to Use Pythagorean Theorem?
The Pythagorean Theorem Calculator simplifies finding the length of the hypotenuse or the missing side of a right-angled triangle. You just have to open the calculatorology Pythagorean theorem calculator, which will ask you the length of two known sides of a right-angled triangle. You can quickly solve geometric problems involving right triangles by entering the lengths of two sides.
- Enter Length of Side A: Input the measurement of one side A of the triangle.
- Enter Length of Side B: Input the measurement of the second side B of the triangle.
Calculation and Results:
The calculator uses the formula c = a2 + b2 to compute the length of the hypotenuse or rearranges to find a missing side if only one side is provided. The result will be the precise length of the hypotenuse or the missing side.
Example;
Suppose you have a right-angled triangle where sides A and B lengths are 5 cm and 12 cm, respectively, and you must find the hypotenuse length. By using our Pythagorean Theorem Calculator, you can determine the hypotenuse efficiently.
Length of Side A: 5 cm
Length of Side B: 12 cm
Solution
After entering the lengths of side A and side B, the calculator processes them with the help of the Pythagorean formula and gives you instant results:
Apply the formula for the hypotenuse: c
a2 +b2 =c2
c = a2 + b2
c = (5)2 + (12)2
c = 25 +144
c = 169
c = 13 cm
Results:
The length of the hypotenuse is 13 cm. This calculation confirms that for a right-angled triangle with sides measuring 5 cm and 12 cm, the hypotenuse will be precisely 13 cm.
Applications of the Pythagorean Theorem
Application | Explanation |
Architecture | Ensures structural integrity and accurate measurements |
Navigation | Used in GPS and mapping systems |
Engineering | Assists in creating precise components |
Sports | Helps in analyzing and improving performance |
Facts About Pythagorean Theorem
- The theorem is strictly for right-angled triangles.
- In a right triangle, the hypotenuse always has more length than the other two sides.
- The theorem can be applied to triangles with non-integer side lengths as well.