1. What is a 45 Degree Right Triangle Calculator?

Definition: This calculator computes either the hypotenuse or leg length of a 45-45-90 right triangle when one value is known.

Purpose: It helps students, engineers, and designers quickly solve for missing dimensions in isosceles right triangles.

2. How Does the Calculator Work?

The calculator uses these formulas:

Where:

• hyp — Hypotenuse (longest side opposite the right angle)
• leg — Either of the two equal sides adjacent to the right angle
• √2 — Approximately 1.41421

Explanation: In a 45-45-90 triangle, the hypotenuse is always √2 times longer than either leg.

3. Importance of 45-45-90 Triangles

Details: These special right triangles are fundamental in geometry, construction, and design, appearing frequently in squares, diamonds, and octagons.

4. Using the Calculator

Tips: Enter either the leg length or hypotenuse (leave the other field blank). The calculator will compute the missing value.

5. Frequently Asked Questions (FAQ)

Q1: Why is the ratio always 1:1:√2?
A: Because both non-right angles are 45°, making the triangle isosceles with equal legs, and the hypotenuse follows from the Pythagorean theorem.

Q2: What units should I use?
A: The calculator works with any consistent units (meters, feet, etc.) - just be sure to use the same unit for both input and output.

Q3: Can I use this for non-45-degree right triangles?
A: No, this calculator is specifically for 45-45-90 triangles. Use our Right Triangle Calculator for other angles.

Q4: How precise are the calculations?
A: Results are precise to 3 decimal places, using √2 ≈ 1.41421356237.

Q5: What practical applications use 45-45-90 triangles?
A: Common in construction (roof framing), quilting (half-square triangles), and engineering (force diagrams).