Hypotenuse Calculator

Formula: c = √(a² + b²)

Hypotenuse
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Triangle Visualization

Right triangle with sides a, b and hypotenuse c

📐 What is a Hypotenuse Calculator?

A Hypotenuse Calculator is a tool that helps you quickly find the longest side of a right triangle without manual calculation. You simply enter the two known sides (a and b), and it instantly calculates the hypotenuse (c) using the Pythagorean theorem.

Instead of solving square roots manually, this calculator gives you fast and accurate results, making it useful for students, engineers, and everyday problem-solving.


📘 How to calculate the hypotenuse of a right triangle?

The hypotenuse is the longest side of a right triangle, located opposite the 90° angle. It is calculated using the Pythagorean theorem:

\[ c = \sqrt{a^2 + b^2} \]

Where:

  • a = one side of the triangle
  • b = second side of the triangle
  • c = hypotenuse (longest side)
how to calculate hypotenuse of a right triangle example 6 8 10

🧮 Example 1 (Basic)

Find the hypotenuse when two sides are small numbers:

  • a = 6
  • b = 8
\[ c = \sqrt{6^2 + 8^2} \] \[ c = \sqrt{36 + 64} = \sqrt{100} = 10 \]

✅ Hypotenuse = 10

📘 Example 2 (Common Exam)

This is a popular Pythagorean triple used in exams:

  • a = 5
  • b = 12
\[ c = \sqrt{5^2 + 12^2} \] \[ c = \sqrt{25 + 144} = \sqrt{169} = 13 \]

✅ Hypotenuse = 13

🏗️ Example 3 (Real-Life Use)

A ladder is placed against a wall:

  • Height (a) = 9 m
  • Distance from wall (b) = 12 m
\[ c = \sqrt{9^2 + 12^2} \] \[ c = \sqrt{81 + 144} = \sqrt{225} = 15 \]

📏 Ladder length = 15 m

📐 Example 4 (Advanced)

Find the hypotenuse for larger values:

  • a = 7
  • b = 24
\[ c = \sqrt{7^2 + 24^2} \] \[ c = \sqrt{49 + 576} = \sqrt{625} = 25 \]

✅ Hypotenuse = 25


🎯 When Do You Need This Calculator?

This calculator is useful in many real-life situations:

FAQ on Hypotenuse Calculator

What is the hypotenuse?

The hypotenuse is the longest side of a right triangle, opposite the 90° angle.

Can the hypotenuse be smaller than other sides?

No, the hypotenuse is always the longest side in a right triangle.

Does this formula work for all triangles?

No, it only works for right-angled triangles.

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