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

Definition: This calculator computes the missing sides of a 45-45-90 right triangle when one side is known.

Purpose: It helps students, engineers, and designers quickly solve for the legs or hypotenuse of this special right triangle.

2. How Does the Calculator Work?

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

Properties: In a 45-45-90 triangle:

• Two legs are equal in length
• Angles are 45°, 45°, and 90°
• Hypotenuse is always \( \sqrt{2} \) times the length of each leg

3. Importance of 45-45-90 Triangle Calculations

Applications: These triangles are fundamental in geometry, construction, and design work, especially for creating square diagonals and isosceles right triangles.

4. Using the Calculator

Tips: Enter either:

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

Only one value is needed - the calculator will compute the others.

5. Frequently Asked Questions (FAQ)

Q1: Why is the hypotenuse √2 times the leg?
A: This comes from the Pythagorean theorem: \( \sqrt{leg^2 + leg^2} = leg \times \sqrt{2} \).

Q2: Are both legs always equal?
A: Yes, by definition in a 45-45-90 triangle, both legs are equal and the angles opposite them are both 45°.

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

Q4: How precise are the calculations?
A: The calculator provides results to 3 decimal places, using PHP's floating-point precision.

Q5: What units should I use?
A: The calculator works with any consistent unit (meters, feet, etc.) as long as you're consistent.