1. What is a 45-45-90 Triangle?

Definition: A 45-45-90 triangle is a special right triangle where the two legs are equal in length and the angles opposite them are both 45 degrees.

Properties: The hypotenuse is always √2 times the length of each leg. The ratio of sides is 1:1:√2.

2. How Does the Calculator Work?

The calculator uses these formulas:

Usage: Enter either the leg length or hypotenuse, and the calculator will compute the missing value.

3. Applications of 45-45-90 Triangles

Common Uses: These triangles are fundamental in geometry, construction, and design. They're used in:

• Creating square diagonal measurements
• Roof framing
• Quilt patterns
• Graphic design layouts

4. Using the Calculator

Tips: Enter either:

• The length of one leg to calculate the hypotenuse and other leg
• The hypotenuse to calculate both legs

All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is the hypotenuse longer than the legs?
A: In right triangles, the hypotenuse is always the longest side. In 45-45-90 triangles, it's exactly √2 (≈1.414) times longer than each leg.

Q2: Can I use this for other right triangles?
A: No, this calculator is specifically for 45-45-90 triangles. Other right triangles have different angle and side relationships.

Q3: How precise are the calculations?
A: Results are precise to 3 decimal places. √2 is approximately 1.41421356237.

Q4: What units should I use?
A: The calculator works with any consistent unit (meters, feet, inches, etc.). Results are shown in the same unit you input.

Q5: What if I enter both values?
A: The calculator will prioritize the leg value and recalculate the hypotenuse based on it.