1. 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 and the sides opposite these angles are equal in length. The sides are in the ratio 1:1:√2.

2. How Does the Calculator Work?

The calculator uses the 45-45-90 triangle formulas:

Where:

• leg — Either of the two equal sides
• hypotenuse — The side opposite the right angle
• √2 — Approximately 1.4142

Explanation: The formulas derive from the Pythagorean theorem, with both legs being equal in length.

3. Properties of 45-45-90 Triangles

Details: In a 45-45-90 triangle:

• The two legs are congruent
• The hypotenuse is √2 times the length of each leg
• The angles are in the ratio 1:1:2 (45°:45°:90°)
• It's half of a square divided diagonally

4. Using the Calculator

Tips: Enter either the length of a leg or the hypotenuse, select which value you entered, and the calculator will compute all three sides of the triangle.

5. Frequently Asked Questions (FAQ)

Q1: What are the applications of 45-45-90 triangles?
A: They're used in construction, engineering, and design where right angles and equal sides are needed, like in diagonal supports or square-based structures.

Q2: How do you derive the 45-45-90 triangle ratios?
A: Using the Pythagorean theorem (a² + b² = c²) where a = b, so c = a√2.

Q3: Can this calculator work with different units?
A: Yes, as long as you're consistent with your units (all in cm, inches, etc.), the ratios will remain the same.

Q4: What's the area formula for a 45-45-90 triangle?
A: Area = (leg × leg)/2 or (hypotenuse²)/4.

Q5: Are there other special right triangles?
A: Yes, the 30-60-90 triangle is another important special right triangle with different side ratios (1:√3:2).