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

A 30-60-90 triangle is a special right triangle where the angles measure 30°, 60°, and 90°. The sides are in a consistent ratio that makes calculations straightforward once you know one side length.

2. How Does the Calculator Work?

The calculator uses the 30-60-90 triangle ratio rules:

Where:

• short — The side opposite the 30° angle (shortest side)
• long — The side opposite the 60° angle
• hyp — The side opposite the 90° angle (hypotenuse, longest side)

Explanation: The hypotenuse is always twice the length of the shortest side, and the longer leg is √3 times the shortest side.

3. Properties of 30-60-90 Triangles

Details: The sides maintain a consistent ratio of 1 : √3 : 2 (short : long : hypotenuse). These triangles are half of an equilateral triangle.

4. Using the Calculator

Tips: Enter any one side length, specify which side it is (short, long, or hypotenuse), and include units if desired. The calculator will compute the other two sides.

5. Frequently Asked Questions (FAQ)

Q1: Why is the ratio always 1:√3:2?
A: This comes from the trigonometric relationships in a 30-60-90 triangle and the properties of equilateral triangles.

Q2: How do I find the area of a 30-60-90 triangle?
A: Area = (short × long) / 2 or (short² × √3) / 2.

Q3: Can this calculator work if I know the perimeter?
A: No, this calculator requires one side length. For perimeter, you'd need to solve algebraically first.

Q4: Are there real-world applications of 30-60-90 triangles?
A: Yes, in construction, engineering, and any field requiring precise angle measurements.

Q5: How does this relate to the 45-45-90 triangle?
A: Both are special right triangles, but with different angle measures and side ratios (1:1:√2 for 45-45-90).