Reverse Hypotenuse Calculator

| Added in Math & Numbers

What is Reverse Hypotenuse and Why Should You Care?

A Reverse Hypotenuse calculation lets you find the unknown side of a right-angled triangle when you know the hypotenuse and one other side. This is useful in construction, navigation, graphic design, and any field that involves geometry.

How to Calculate Reverse Hypotenuse

The standard Pythagorean theorem states:

[\text{Hypotenuse} = \sqrt{\text{Side 1}^{2} + \text{Side 2}^{2}}]

To find an unknown side, rearrange the formula:

[\text{Unknown Side} = \sqrt{\text{Hypotenuse}^{2} - \text{Known Side}^{2}}]

Where:

  • Unknown Side is the side you are looking for.
  • Hypotenuse is the side opposite the right angle.
  • Known Side is the side length you already know.

Calculation Example

Example 1

Given a hypotenuse of 40 and a known side of 15:

[\text{Unknown Side} = \sqrt{40^{2} - 15^{2}} = \sqrt{1600 - 225} = \sqrt{1375} \approx 37.08]

The missing side is approximately 37.08.

Example 2

Given a hypotenuse of 25 and a known side of 7:

[\text{Unknown Side} = \sqrt{25^{2} - 7^{2}} = \sqrt{625 - 49} = \sqrt{576} = 24]

The missing side is exactly 24.

Frequently Asked Questions

A Reverse Hypotenuse calculation finds the unknown side of a right triangle when you know the hypotenuse and one other side. It reverses the Pythagorean theorem.

It uses the formula: Unknown Side equals the square root of the hypotenuse squared minus the known side squared.

In a right triangle, the hypotenuse is always the longest side. If the known side were longer, no valid triangle could exist.

The unit does not affect the calculation, but both inputs must use the same unit. The result will be in that same unit.

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