Pythagoras Theorem Calculator

Published on: September 8, 2024
Final Answer: Free • Full Steps: Plus

This Pythagoras Theorem Calculator helps you find the hypotenuse of a right triangle when the other two sides are known. It uses the formula c = √(a² + b²), where a and b are the shorter sides, c is the hypotenuse, and the answer is written in units. First square the two known sides, add them together, and then take the square root to get the hypotenuse. It is a simple way to check answers, understand Pythagoras’ theorem, and practise basic geometry step by step.

Right triangle with legs a, b and hypotenuse c

In the diagram, the legs are a and b, and the hypotenuse is c.

Step-by-step method

  1. Identify what is given.
  2. Write the formula.
  3. Substitute the values and calculate the hypotenuse.

Formula:

\(c = \sqrt{a^{2} + b^{2}}\)

Example 1:

\(a = 3, b = 4\)

Step 1 - Identify what is given.

In this problem: The given side lengths are \(a = 3\) and \(b = 4\).

\(a = 3,\; b = 4\)

Step 2 - Write the formula.

In this problem: Use the Pythagoras theorem formula: \(c = \sqrt{a^{2} + b^{2}}\).

\(c = \sqrt{a^{2} + b^{2}}\)

Step 3 - Substitute the values and calculate the hypotenuse.

In this problem: Substitute \(a = 3\) and \(b = 4\): \(c = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5\).

\(c = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5\)

Final answer:

\(c = 5\)

Example 2:

\(a = 6.5, b = 4.25\)

Step 1 - Identify what is given.

In this problem: The given side lengths are \(a = 6.5\) and \(b = 4.25\).

\(a = 6.5,\; b = 4.25\)

Step 2 - Write the formula.

In this problem: Use the Pythagoras theorem formula: \(c = \sqrt{a^{2} + b^{2}}\).

\(c = \sqrt{a^{2} + b^{2}}\)

Step 3 - Substitute the values and calculate the hypotenuse.

In this problem: Substitute \(a = 6.5\) and \(b = 4.25\): \(c = \sqrt{6.5^{2} + 4.25^{2}} = \sqrt{60.3125} \approx 7.77\).

\(c = \sqrt{6.5^{2} + 4.25^{2}} = \sqrt{60.3125} \approx 7.77\)

Final answer:

\(c \approx 7.77\)