1. What is a 30-60-90 Triangle?

Definition: A special right triangle with angles measuring 30°, 60°, and 90° with consistent side length ratios.

Purpose: These triangles are common in geometry, trigonometry, and real-world applications like construction and engineering.

2. How Does the Calculator Work?

The calculator uses the standard ratio:

Where:

• \( x \) — Shortest side (opposite 30° angle)
• \( x\sqrt{3} \) — Longer leg (opposite 60° angle)
• \( 2x \) — Hypotenuse (opposite 90° angle)

Explanation: Enter any one side length to calculate the other two sides based on these fixed ratios.

3. Importance of 30-60-90 Triangles

Details: These triangles appear frequently in trigonometry problems, architectural designs, and engineering calculations.

4. Using the Calculator

Tips: Enter the length of the shortest side (opposite the 30° angle) to calculate the other two sides. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Can I enter a different side than the short leg?
A: This calculator is designed for the short leg input. For other inputs, different calculations would be needed.

Q2: Why are the sides in this ratio?
A: The ratios come from the trigonometric relationships in a 30-60-90 triangle derived from an equilateral triangle.

Q3: What units should I use?
A: Any consistent unit can be used (meters, feet, etc.) as long as all measurements use the same unit.

Q4: How accurate are the results?
A: Results are mathematically precise based on the input value and the √3 ratio.

Q5: Can this be used for other special triangles?
A: No, this is specific to 30-60-90 triangles. A different calculator would be needed for 45-45-90 triangles.