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, and the two legs are always equal in length.

2. How Does the Calculator Work?

The calculator uses these formulas:

Explanation:

• To find the hypotenuse when you know a leg, multiply by √2 (approximately 1.414)
• To find a leg when you know the hypotenuse, divide by √2

3. Applications of 45-45-90 Triangles

Details: These triangles are commonly used in construction, engineering, and design for creating square corners and diagonal measurements.

4. Using the Calculator

Tips:

• Enter your known value (either leg or hypotenuse)
• Select what you want to calculate
• The calculator will automatically compute the unknown side

5. Frequently Asked Questions (FAQ)

Q1: Why is the ratio always 1:1:√2?
A: This comes from the Pythagorean theorem. For a right triangle with legs of length 1: 1² + 1² = hypotenuse² → hypotenuse = √2.

Q2: How accurate are the calculations?
A: The calculator uses precise mathematical relationships, so results are mathematically exact (though displayed to 3 decimal places).

Q3: Can I use this for other triangle types?
A: No, this calculator is specifically for 45-45-90 triangles. Other triangles have different relationships.

Q4: What units should I use?
A: The calculator works with any consistent unit (meters, feet, etc.), but results will be in the same unit as your input.

Q5: How do I measure the angles?
A: Use a protractor to confirm 45° angles, or verify that both non-right angles are equal in an isosceles right triangle.