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.

Properties: The sides are always in the ratio 1 : √3 : 2 (shortest : medium : hypotenuse).

2. How Does the Calculator Work?

The calculator uses the standard ratios:

Where:

• \( x \) — Length of the shortest side (opposite 30° angle)
• \( x\sqrt{3} \) — Length of the medium side (opposite 60° angle)
• \( 2x \) — Length of the hypotenuse (opposite 90° angle)

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

3. Applications of 30-60-90 Triangles

Uses: Common in trigonometry, engineering, architecture, and any field requiring precise geometric calculations.

4. Using the Calculator

Tips: Enter the length of the shortest side (x) in meters. The calculator will automatically compute the medium side (x√3) and hypotenuse (2x).

5. Frequently Asked Questions (FAQ)

Q1: Can I enter a different side length?
A: This version calculates from the shortest side. Future versions may allow input of any side.

Q2: Why are the ratios always the same?
A: The angles determine the side ratios in any 30-60-90 triangle, regardless of size.

Q3: What units does this use?
A: The calculator uses meters by default, but any unit can be used as long as you're consistent.

Q4: How accurate are the results?
A: Results are mathematically precise, displayed to 3 decimal places.

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