# Pythagorean Theorem Calculator

Pythagorean Theorem Calculator helps to find the unknown side length of a right-angled triangle when two side lengths are known. The Pythagorean Theorem gives the relation among the three sides of a right triangle and hence, is one of the most fundamental concepts of Geometry.

## What is the Pythagorean Theorem Calculator?

Pythagorean Theorem Calculator is an online tool to determine any side of a right-angled triangle when the other two sides are given. Pythagorean Theorem sees use in several sister subjects such as Trigonometry. To use the * Pythagorean Theorem calculator *choose the side to be computed from the drop-down menu and enter the values in the input boxes.

## What is Pythagorean Theorem?

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The hypotenuse is the side of the triangle opposite to the right angle. Furthermore, the length of the hypotenuse is greater than the length of the altitude and the length of the base. However, the length of the hypotenuse will be lesser than the sum of lengths of the remaining two sides. The Pythagorean Theorem is used in the field of architecture to ensure that the structures created are strong and robust.

In the given \(\Delta ABC \),

**\[\begin{align}
\text{BC}^2 &= \text{AB}^2 +\text{AC}^2
\end{align}\]**

where,

- \( \text{AB}\) is the base,
- \( \text{AC}\) is the altitude or the height, and
- \( \text{BC}\) is the hypotenuse.

To calculate the hypotenuse we simply plug in the values into the above equation. However, if we want to find the value of the base or the altitude we have to follow the steps given below.

- Suppose we need to determine the value of the altitude. We have to shift the base (AB
^{2}) to the left-hand side of the equation. - We then subtract the base from the hypotenuse (BC
^{2}- AB^{2}). - We now have to take the square root of this value to get the length of the altitude.
- The same steps can be used if we have to find the length of the base.

## How to Use the Pythagorean Theorem Calculator?

Follow these steps which will help you to use the calculator.

**Step 1:**Select the side of the right-angled triangle to be calculated, from the drop-down list.**Step 2:**Enter the value for the other two sides in the corresponding input boxes.**Step 3:**Click on "**Calculate**" to find the unknown side of the triangle.**Step 4:**Click on "**Reset**" to clear the fields and enter the new values.

**Solved Examples on Pythagorean Theorem**

**Example 1:** A right-angled triangle ABC, has base BC = 12 units, height AB = 5 units. What is the length of AC?

**Solution:**

By Pythagoras theorem we know that,

AB^{2} + BC^{2} = AC^{2}

AC^{2} = 5^{2 }+ 12^{2}

AC = (5^{2} + 12^{2})^{½} = **√**(5^{2} + 12^{2})

AC = 13 units.

**Answer: The length of AC is 13 units.**

**Example 2:** A right-angled triangle PQR, has angle Q = 90°. PQ = 8 units. PR = 10 units. Find QR.

**Solution:**

By Pythagoras Theorem we know that,

PR^{2}= PQ^{2} + QR^{2}^{ }

10^{2} = 8^{2 } + QR^{2}

QR^{2} = 10^{2} - 8^{2 }

QR = (10^{2} - 8^{2})^{½} = √(10^{2} - 8^{2})

QR = 6 units.** **

**Answer: The length of QR is 6 units.**

Similarly, you can use the Pythagorean Calculator calculator to find the hypotenuse of right-angled triangles with:

- Side a = 6 units and side b = 8 units.
- Side a = 12 units and side b = 5 units.
- Side a = 3 units and side b = 4 units.

**ā Math Calculators:**