Calculate Length of Triagle 45 Degrees

Calculating the length of a triangle with a 45-degree angle involves understanding the relationship between the sides and angles of a right triangle. This calculator provides a quick and accurate way to determine the missing side length when you know one side and the 45-degree angle.

How to Use This Calculator

Using our calculator is simple:

Enter the length of the known side in the input field.
Select the units (inches, centimeters, meters, etc.) from the dropdown menu.
Click the "Calculate" button to see the result.
Review the detailed explanation of the calculation.

The calculator will display the length of the other two sides of the triangle, which are equal in a 45-45-90 triangle.

The Formula

In a 45-45-90 triangle, the two legs are equal in length, and the hypotenuse is √2 times the length of each leg. The formula for calculating the sides is:

If you know the length of one leg (L):

Other leg = L

Hypotenuse = L × √2

If you know the hypotenuse (H):

Each leg = H / √2

This relationship is derived from the properties of a 45-45-90 triangle, where the angles are 45°, 45°, and 90°, and the sides are in the ratio 1:1:√2.

Worked Example

Let's say you have a 45-45-90 triangle with one leg measuring 5 inches. Using the formula:

Other leg = 5 inches

Hypotenuse = 5 × √2 ≈ 7.071 inches

So, the other leg is also 5 inches, and the hypotenuse is approximately 7.071 inches.

Frequently Asked Questions

What is a 45-45-90 triangle?: A 45-45-90 triangle is a special right triangle where the two non-right angles are both 45 degrees. The sides opposite these angles are equal in length, and the hypotenuse is √2 times the length of each leg.
How do I calculate the sides of a 45-45-90 triangle?: Use the formulas provided in the "The Formula" section. If you know one leg, the other leg is equal, and the hypotenuse is leg × √2. If you know the hypotenuse, each leg is hypotenuse / √2.
Can I use this calculator for non-right triangles?: No, this calculator is specifically designed for 45-45-90 triangles. For other types of triangles, you would need a different calculator or method.
What units should I use with this calculator?: You can use any unit of length (inches, centimeters, meters, etc.), as long as you're consistent throughout the calculation.