30-60-90 Degree Triangle Calculator by Tons of Concrete

30-60-90 Triangle Properties:

\[ \text{Sides: } x \text{ (opp 30°), } x\sqrt{3} \text{ (opp 60°), } 2x \text{ (hypotenuse)} \]

30° Side (shortest): meters

60° Side (medium): meters

Hypotenuse: meters

Unit Converter ▲

Unit Converter ▼

From:	To:

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

Definition: A special right triangle where the angles measure 30°, 60°, and 90° with sides in a consistent ratio.

Properties: The sides opposite these angles follow the ratio: 1 : √3 : 2 (shortest : medium : hypotenuse).

2. How Does the Calculator Work?

The calculator uses the standard ratio:

\[ x : x\sqrt{3} : 2x \]

Where:

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

Explanation: Enter any one side length and specify which side it is, and the calculator determines the other two sides.

3. Importance of 30-60-90 Triangles

Details: These triangles are fundamental in geometry, trigonometry, and various engineering applications due to their predictable side ratios.

4. Using the Calculator

Tips: Enter the known side length and select whether it's the short side (30° opposite), medium side (60° opposite), or hypotenuse.

5. Frequently Asked Questions (FAQ)

Q1: Why is the ratio always 1 : √3 : 2?
A: This ratio comes from the properties of half an equilateral triangle and is consistent for all 30-60-90 triangles.

Q2: How do I find the area of a 30-60-90 triangle?
A: Area = (short side × medium side) / 2 = (x × x√3)/2 = (x²√3)/2.

Q3: Can I use this for other triangles?
A: No, this calculator is specific to 30-60-90 triangles. Other triangles have different properties.

Q4: What if I know the perimeter?
A: First calculate x from perimeter = x + x√3 + 2x, then use x to find all sides.

Q5: How accurate are the calculations?
A: The calculations are mathematically precise, though displayed results are rounded to 3 decimal places.