Calculation: A Pythagorean Theorem Calculator is a useful tool for solving problems related to right-angled triangles. It helps you easily calculate the length of a missing side when you know the lengths of the other two sides.
What Does Pythagorean Theorem Calculator Do?
The Pythagorean Theorem Calculator applies the Pythagorean Theorem, which is a fundamental principle in geometry, to determine the missing side of a right triangle. If you know the lengths of two sides, you can use this calculator to find the third side, whether it is the hypotenuse or one of the legs of the triangle.
Pythagorean Theorem Calculator Formula
To calculate the length of the missing side in a right-angled triangle, use the following formula:
c² = a² + b²
Where:
- c is the length of the hypotenuse (the side opposite the right angle),
- a and b are the lengths of the other two sides (legs of the triangle).
If you need to find the length of a leg (a or b), you can rearrange the formula as follows:
a² = c² - b²
b² = c² - a²
Pythagorean Theorem Calculation Examples
Example 1: Finding the Hypotenuse
Let’s say we have a right-angled triangle with legs of 3 cm and 4 cm, and we need to find the length of the hypotenuse.
- Start with the formula: c² = a² + b².
- Plug in the values: c² = 3² + 4².
- Simplify the calculation: c² = 9 + 16.
- Find the square root: c = √25 = 5 cm.
So, the length of the hypotenuse is 5 cm.
Example 2: Finding a Missing Leg
Suppose we have a right-angled triangle with a hypotenuse of 10 cm and one leg of 6 cm, and we need to find the length of the other leg.
- Start with the formula: a² = c² – b².
- Plug in the values: a² = 10² – 6².
- Simplify the calculation: a² = 100 – 36.
- Find the square root: a = √64 = 8 cm.
So, the length of the missing leg is 8 cm.
The Pythagorean Theorem Calculator is an essential tool for anyone studying geometry or solving real-world problems involving right-angled triangles, allowing you to quickly and accurately determine the missing side using the Pythagorean Theorem.