Calculator Inputs
Formula Used
Core formulas
Pythagorean theorem: a² + b² = c²
Area: Area = a × b ÷ 2
Perimeter: P = a + b + c
Angle A: A = atan(a ÷ b)
Height to hypotenuse: h = a × b ÷ c
Inradius: r = (a + b - c) ÷ 2
Circumradius: R = c ÷ 2
Formulas from your last calculation
Submit values to see the exact formulas used for your case.
How to Use This Calculator
- Select the method that matches your known values.
- Enter exactly two sides, or enter one side with angle A.
- You can also enter area with one known side.
- Add a unit label, such as cm, m, in, or ft.
- Choose decimal places for the final answer.
- Use the scale multiplier when resizing a similar triangle.
- Press the calculate button to view results above the form.
- Download the results as CSV or PDF when needed.
Example Data Table
| Known Values | Method | Leg a | Leg b | Hypotenuse c | Area | Angles |
|---|---|---|---|---|---|---|
| a = 3, b = 4 | Two sides | 3 | 4 | 5 | 6 | 36.87°, 53.13° |
| c = 10, A = 30° | Side and angle | 5 | 8.6603 | 10 | 21.6506 | 30°, 60° |
| Area = 24, a = 6 | Area and side | 6 | 8 | 10 | 24 | 36.87°, 53.13° |
Understanding Right Triangle Side Lengths
Right triangles are useful because one angle is always ninety degrees. That fixed angle creates predictable links between the three sides. The two shorter sides are called legs. The longest side is the hypotenuse. It always sits opposite the right angle.
Why Side Lengths Matter
Side lengths help you measure ramps, ladders, screens, roofs, braces, and paths. They also help in school geometry. A missing side can be found when enough information is known. The most common method is the Pythagorean theorem. Trigonometric ratios are also helpful when an angle is known.
Using Two Known Sides
When both legs are known, square each leg. Add the squares. Then take the square root. The answer is the hypotenuse. When one leg and the hypotenuse are known, square the hypotenuse. Subtract the known leg square. Then take the square root. The answer is the missing leg.
Using One Side and an Angle
Sometimes only one side and one acute angle are available. Sine, cosine, and tangent connect these values. Sine compares the opposite side with the hypotenuse. Cosine compares the adjacent side with the hypotenuse. Tangent compares the opposite side with the adjacent side. This calculator uses those ratios to complete the triangle.
Reading the Extra Results
The calculator also finds area, perimeter, angles, height to the hypotenuse, inradius, and circumradius. These values explain the triangle more fully. Area shows covered space. Perimeter shows outside distance. Height to the hypotenuse helps in altitude problems. Radius values are useful in circle relationships.
Accuracy Tips
Use the same unit for every side. Do not mix inches and feet. Choose a sensible precision level. Higher precision is useful for design work. Lower precision is easier for homework. Always check that the hypotenuse is the largest side. Also check that both acute angles add to ninety degrees. These checks help catch typing mistakes quickly.
Practical Example
Assume a ladder reaches a wall at a right angle to the ground. The ladder is the hypotenuse. The wall height is one leg. The ground distance is the other leg. With two values, the third value becomes clear. This makes planning safer and easier before cutting or buying materials.
FAQs
1. What is a right triangle?
A right triangle has one angle measuring exactly ninety degrees. The two sides that meet at that angle are legs. The longest side is the hypotenuse.
2. Which side is the hypotenuse?
The hypotenuse is always opposite the right angle. It is also the longest side of the right triangle.
3. Can I enter any two sides?
Yes. Enter any two positive side lengths in the two-side method. Leave the unknown side blank. The tool calculates the missing value.
4. Can I use an angle?
Yes. Select the side and angle method. Enter one acute angle and one known side. The calculator then uses trigonometric ratios.
5. Why must the angle be less than ninety degrees?
A right triangle already contains one ninety-degree angle. The other two angles must be acute and must add to ninety degrees.
6. What does the scale multiplier do?
It resizes the solved triangle. A value of 2 doubles every side. Area changes by the square of the multiplier.
7. Why is my input rejected?
The calculator rejects impossible triangles. For example, a hypotenuse cannot be shorter than a leg. Values must also be positive.
8. Are the results exact?
Results are calculated using standard formulas. Decimal output is rounded based on your selected precision. Increase decimal places for tighter estimates.