Sides of a 30-60-90 Triangle Calculator

30-60-90 Triangle Side Ratios:

\[ \text{Short leg} = x \] \[ \text{Long leg} = x\sqrt{3} \] \[ \text{Hypotenuse} = 2x \]

Long Leg (x√3):

Hypotenuse (2x):

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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 (short leg : long leg : hypotenuse).

2. How Does the Calculator Work?

The calculator uses the fixed ratios:

\[ \text{Long leg} = \text{Short leg} \times \sqrt{3} \] \[ \text{Hypotenuse} = \text{Short leg} \times 2 \]

Where:

Short leg (x) — Side opposite the 30° angle
Long leg (x√3) — Side opposite the 60° angle
Hypotenuse (2x) — Side opposite the 90° angle

3. Applications of 30-60-90 Triangles

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

4. Using the Calculator

Tips: Simply enter the length of the short leg (x) to calculate the other sides. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Can I calculate from a different side?
A: Yes, if you know another side, divide it by its ratio multiplier (√3 for long leg, 2 for hypotenuse) to find x.

Q2: What units does this use?
A: The calculator works with any consistent units (meters, feet, etc.) - just enter your measurement.

Q3: Why are these ratios constant?
A: They derive from the trigonometric functions of 30° and 60° angles in a right triangle.

Q4: How accurate are the results?
A: Results are mathematically precise, though displayed with 3 decimal places for readability.

Q5: Can this be used for other triangles?
A: No, these ratios only apply to 30-60-90 triangles. Other triangles require different calculations.