Hypotenuse of a Triangle Calculator (Pythagorean Theorem Calculator)

Last Updated : 21 Mar, 2024

Hypotenuse Calculator: In geometry, the hypotenuse is a fundamental concept, especially in right-angled triangles. It’s the side opposite the right angle and is crucial for various calculations and real-world applications. GeeksforGeeks offers a free online hypotenuse calculator tool. This calculator helps you to find the hypotenuse of a right angle triangle. Their tool is easy to use and makes sure you get accurate results. It’s a handy calculator for anyone, in any area like engineering, physics etc. It also helps students and professionals with their everyday math problems.

How to use Hypotenuse Calculator

Calculating the hypotenuse manually involves using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

1. Input Side Lengths: Start by identifying the lengths of the two sides adjacent to the right angle (the legs of the triangle).

2. Apply Pythagorean Theorem: Square the lengths of the two legs, then add them together. Finally, take the square root of the sum to find the length of the hypotenuse.

3. Calculate Hypotenuse: The calculated value represents the length of the hypotenuse in the right-angled triangle.

Hypotenuse Definition

The hypotenuse is all about right triangles! The hypotenuse of a right triangle is the side opposite the right angle. It’s the longest side of the triangle and is always directly across from the right angle.

Key points about hypotenuse:

Longest side
Opposite the right angle
Pythagorean Theorem

What is a Hypotenuse Calculator?

A Hypotenuse Calculator is a digital guide that assists individuals in computing the length of the hypotenuse in a right-angled triangle without having to perform manual calculations. It automates the process, making it quick and accurate.

The Pythagorean theorem is a formula used to find the hypotenuse of a right triangle. To use hypotenuse calculator, the formula looks like this:

The square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Hypotenuse^2 = (Base^2 + Height^2)

How does Hypotenuse Calculator Work

Let’s consider a right triangle with side lengths of 3 units and 4 units.

Input Side Lengths:

The lengths of the two legs are 3 units and 4 units.

Apply Pythagorean Theorem:

Square the lengths of the legs: 3^2 = 9 and 4^2 = 16.

Then, add these squares together: 9 + 16 = 25.

Calculate Hypotenuse:

Take the square root of the sum: Sqrt 25 = 5

So, in this example, the length of the hypotenuse is 5 units.

Hypotenuse Calculator Table

Here’s a table showing the lengths of the hypotenuse for different right triangles:

Side Lengths	Hypotenuse Length
3, 4	5
5, 12	13
8, 15	17
7, 24	25
20, 21	29

Solved Examples on Hypotenuse Calculator

Example 1: Side lengths: 6 units and 8 units

Applying Pythagorean theorem: 6^2 + 8^2 = 36 + 64 = 100

Hypotenuse length: sqrt 100 = 10 units

Example 2: Side lengths: 9 units and 12 units

Applying Pythagorean theorem: 9^2 + 12^2 = 81 + 144 = 225

Hypotenuse length: sqrt 225 = 15 units

Example 3: Side lengths: 15 units and 20 units

Applying Pythagorean theorem: 15^2 + 20^2 = 225 + 400 = 625

Hypotenuse length: 625 = 25 units

3 Practice Questions on Hypotenuse Calculator

Q1. In a right triangle with legs measuring 7 units and 24 units, what is the length of the hypotenuse?

Q2. If the legs of a right triangle measure 10 units and 24 units, what is the length of the hypotenuse?

Q3. Determine the length of the hypotenuse in a right triangle with legs measuring 4 units and 3 units.

Conclusion

The Hypotenuse Calculator is a valuable tool for quickly and accurately determining the length of the hypotenuse in a right-angled triangle. Whether you’re a student studying geometry or a professional involved in architectural or engineering projects, this guide simplifies the calculation process and gives accurate results. Understanding hypotenuse calculator about the manual calculations behind the tool can deepen one’s understanding of geometric concepts and improve problem-solving skills.