Side Ratio of a 30-60-90 Triangle

30-60-90 Triangle Ratio Formula:

\[ 1 : \sqrt{3} : 2 \]

Medium Side (Opposite 60°):

Hypotenuse (Opposite 90°):

Definition: A special right triangle where the angles measure 30°, 60°, and 90°. The sides are always in the ratio 1 : √3 : 2.

Purpose: This calculator helps find the lengths of all sides when you know one side of a 30-60-90 triangle.

The calculator uses the fixed ratio:

\[ 1 : \sqrt{3} : 2 \]

Where:

Explanation: Multiply the known side by these ratios to find the other sides.

Details: These triangles are fundamental in geometry, trigonometry, and many real-world applications like construction and engineering.

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

Q1: What if I know the hypotenuse instead?
A: Divide the hypotenuse by 2 to get the shortest side, then multiply by √3 for the medium side.

Q2: What if I know the medium side?
A: Divide the medium side by √3 to get the shortest side, then multiply by 2 for the hypotenuse.

Q3: Why is this ratio important?
A: It allows quick calculation of all sides when one is known, without needing trigonometric functions.

Q4: Can this be used for any triangle?
A: No, only for 30-60-90 triangles. Other triangles have different properties.

Q5: How accurate are the results?
A: The results are mathematically precise based on the input value and the fixed ratio.