Enter Triangle Values
Example Data Table
| Case | Known Values | Method | Expected Use |
|---|---|---|---|
| SSS | a = 7, b = 9, c = 11 | Law of Cosines | Find all angles and area |
| SAS | b = 8, c = 10, A = 50 | Law of Cosines | Find side a first |
| AAS | A = 42, B = 68, a = 12 | Law of Sines | Find remaining sides |
| SSA | A = 35, a = 9, b = 12 | Ambiguous sine case | Check one or two solutions |
Formula Used
Law of Cosines: a² = b² + c² - 2bc cos(A). Similar forms solve b and c.
Law of Sines: a / sin(A) = b / sin(B) = c / sin(C).
Angle Sum: A + B + C = 180 degrees.
Heron’s Formula: Area = √[s(s - a)(s - b)(s - c)], where s = (a + b + c) / 2.
Inradius: r = Area / s. Circumradius: R = abc / (4 × Area).
Altitude: h = 2 × Area / base. Median: mₐ = ½√(2b² + 2c² - a²).
How to Use This Calculator
- Label the triangle first. Side a must sit opposite angle A.
- Enter all known sides and angles. Leave unknown fields blank.
- Select degrees or radians before entering angle values.
- Choose decimal places and a unit label for the report.
- Press the calculate button. The result appears above the form.
- Use CSV for spreadsheet records or PDF for sharing.
Triangle Side Calculation Guide
A triangle is fully defined when enough connected facts are known. This calculator helps convert those facts into missing sides, angles, area, and supporting measurements. You can enter three sides, two sides with an included angle, two angles with one side, or an ambiguous side side angle case.
Why Triangle Solving Matters
Triangle solving appears in geometry, surveying, design, navigation, roofing, fabrication, and classroom work. A small input mistake can change a side length greatly. That is why the calculator also reports classification, area, perimeter, radii, altitudes, medians, and angle bisectors. These extra values help users review whether the result makes practical sense.
Input Flexibility
The tool uses standard labels. Side a is opposite angle A. Side b is opposite angle B. Side c is opposite angle C. You may leave unknown fields blank. The solver reads the entered values and chooses a suitable rule. When a side side angle case creates two valid triangles, both solutions are displayed.
Result Quality
Every solved triangle must pass the triangle inequality. The angle total must also be close to one hundred eighty degrees. The calculator performs these checks before showing final values. It also gives a method name and short calculation notes, so the result is easier to verify.
Best Practices
Use consistent units for all side entries. Do not mix centimeters with meters unless you convert first. Choose degrees unless your source values are in radians. Increase decimal places when working with small sides or technical drawings. Round the final answer only after checking all important measurements.
Practical Use
Students can use this page to compare homework steps. Builders can estimate bracing and roof values. Surveyors can test measured distances. Designers can confirm a triangular layout before cutting material. The CSV option is useful for records. The PDF option is useful for sharing a clean report.
Final Note
Triangle calculations are reliable when inputs are reliable. Measure carefully, label each side correctly, and keep angle positions clear. After solving, compare the triangle type and area with your expectation. This simple review catches most entry mistakes before the result is used. Save inputs and outputs when documenting technical work for later review. This improves traceability and audit confidence.
FAQs
1. What values can this calculator solve?
It can solve SSS, SAS, ASA, AAS, and many SSA cases. Enter known sides and angles. Leave unknown fields blank. The result shows sides, angles, area, perimeter, and related measurements.
2. What does side a mean?
Side a is opposite angle A. Side b is opposite angle B. Side c is opposite angle C. Correct labeling is important because the sine and cosine rules depend on opposite pairs.
3. Can I enter radians?
Yes. Select radians from the angle unit field before calculating. The calculator converts radians internally, solves the triangle, and returns angle results in your selected unit.
4. Why are two SSA answers shown?
Some side side angle inputs create an ambiguous case. The same known values may form two different triangles. When both are valid, the calculator displays both solutions for review.
5. Why did I get a triangle inequality error?
The triangle inequality requires any two sides to be longer than the third side. If this condition fails, the entered side lengths cannot form a valid triangle.
6. Does the unit label affect calculations?
No. The unit label is only used in the displayed report. All side values must still use the same unit before you enter them into the calculator.
7. How is the area calculated?
After the sides are solved, the calculator uses Heron’s formula. It first finds the semiperimeter, then applies the square root area formula for the three side lengths.
8. Can I export the answer?
Yes. After calculation, use the CSV button for spreadsheet data. Use the PDF button for a simple printable report with result rows and solved measurements.