What Is a Free 30-60-90 Special Right Triangle Calculator?
A Free 30-60-90 Special Right Triangle Calculator is an online mathematics tool that calculates the missing side lengths of a 30°-60°-90° right triangle. It uses the special relationship between the three sides to quickly solve geometry and trigonometry problems.Drag the points
40°
50°AdjacentOppositeHypotenuse
Angles 90°, 40°, and 50° include one fixed right angle
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What Is a 30-60-90 Triangle?
A 30-60-90 triangle is a special right triangle with angles of: 30∘,60∘,90∘30^\circ,\quad 60^\circ,\quad 90^\circ
Its sides always follow the ratio: 1:3:21:\sqrt{3}:2
The sides correspond to:
- Opposite 30°: xx
- Opposite 60°: x3x\sqrt{3}
- Hypotenuse: 2x2x
30-60-90 Triangle Formula
If the shortest side is xx: Short Leg=x\text{Short Leg}=x Long Leg=x3\text{Long Leg}=x\sqrt3 Hypotenuse=2x\text{Hypotenuse}=2x
Example
Suppose the shortest side is 5.
The long leg is: 53≈8.66035\sqrt3\approx8.6603
The hypotenuse is: 2(5)=102(5)=10
Therefore, the three sides are approximately:
5, 8.6603, and 10
How a Free Calculator Works
A typical 30-60-90 Triangle Calculator allows you to:
- Enter a known side length.
- Identify which side is known.
- Calculate the two missing sides.
- Display the results instantly.
- Check the mathematical relationship between the sides.
Why Use a 30-60-90 Triangle Calculator?
This calculator can be useful for:
- Geometry homework
- Trigonometry
- Algebra
- Construction calculations
- Engineering
- Physics
- Finding missing triangle dimensions
- Checking manual calculations
- Learning special right-triangle relationships
Key Relationship
The most important fact to remember is: 1:3:2\boxed{1:\sqrt3:2}
This means that if the shortest side is known, you can quickly determine both the longer leg and the hypotenuse.
In simple terms: a Free 30-60-90 Special Right Triangle Calculator helps you quickly find missing side lengths in a 30°-60°-90° triangle using its fixed 1 : √3 : 2 side ratio.
Explore the 30-60-90 triangle
