Enter Triangle Values
Use standard notation. Side a is opposite angle A. Side b is opposite angle B. Side c is opposite angle C.
Example Data Table
| Method | Input Values | Expected Use | Calculated Output |
|---|---|---|---|
| SSS | a = 7, b = 8, c = 9 | Find all angles from three sides. | A, B, C, area, perimeter |
| SAS | a = 10, b = 12, C = 45° | Use two sides with included angle. | Missing side and both remaining angles |
| ASA/AAS | A = 50°, B = 60°, c = 15 | Find third angle and all sides. | C, sides a and b, area |
| SSA | a = 10, b = 8, A = 40° | Check possible ambiguous cases. | One or two possible triangles |
Formula Used
For three known sides, the calculator uses the Law of Cosines:
A = cos⁻¹((b² + c² - a²) / 2bc).
The same pattern is used for angles B and C.
For two angles, the third angle is:
C = 180° - A - B.
Then the Law of Sines is used:
a / sin(A) = b / sin(B) = c / sin(C).
For SAS, the missing side is:
c² = a² + b² - 2ab cos(C).
After that, all angles are found from side lengths.
Area is calculated with Heron’s formula:
Area = √(s(s-a)(s-b)(s-c)),
where s = (a+b+c)/2.
How to Use This Calculator
- Select the triangle method that matches your known values.
- Enter side lengths and angles in degrees.
- Add a unit label, such as cm, m, ft, or inches.
- Press the calculate button to show results above the form.
- Review angles, sides, area, perimeter, and classifications.
- Use CSV or PDF buttons to save the result.
Triangle Angle Calculator Guide
What This Tool Does
A triangle angle calculator helps solve missing triangle measurements. It is useful when a drawing gives only partial data. You may know three sides. You may know two sides and one included angle. You may also know two angles and one side. This page handles those common geometry cases.
Why Triangle Angles Matter
Triangle angles are important in design, mapping, construction, and study. Every triangle has an angle sum of 180 degrees. That simple rule helps check many answers. Yet real problems often need more than subtraction. Side relationships must also match the triangle shape.
Advanced Solving Options
This calculator supports SSS, SAS, ASA, AAS, and SSA style inputs. The SSA case can be tricky. Sometimes it creates two valid triangles. Sometimes it creates one. Sometimes no triangle exists. The calculator checks those cases and reports valid solutions.
Extra Geometry Details
The result includes more than angles. It also shows side lengths, perimeter, area, heights, inradius, and circumradius. These values help users compare shapes quickly. The classification labels show whether the triangle is scalene, isosceles, or equilateral. They also show whether it is acute, right, or obtuse.
Good Data Improves Results
Use accurate input values for reliable output. Keep units consistent across all side fields. Do not mix meters with feet unless values are converted first. Enter angles in degrees. Avoid rounded construction data when exact measurements are available. Small input changes can shift final angles.
Practical Uses
Students can check trigonometry homework. Builders can review roof, frame, or layout triangles. Surveyors can inspect field measurements. Designers can test proportional shapes. The export options make sharing easier. Saved results are also useful for records and project notes.
FAQs
1. What does side a mean?
Side a is opposite angle A. Side b is opposite angle B. Side c is opposite angle C. This notation keeps formulas clear.
2. Can this calculator solve three-side triangles?
Yes. Choose the SSS method. Enter side a, side b, and side c. The calculator then uses the Law of Cosines.
3. What is the SSA ambiguous case?
SSA may create zero, one, or two valid triangles. The calculator checks both possible angle arrangements and lists every valid result.
4. Are angles entered in degrees?
Yes. Enter every angle in degrees. The calculator converts values internally when sine, cosine, and inverse functions are needed.
5. Can I use any side unit?
Yes. You can use cm, m, ft, inches, or another unit. Keep all side values in the same unit.
6. Why did I get no triangle result?
Your sides or angles may not form a valid triangle. Three sides must satisfy the triangle inequality. Angles must remain below 180 degrees.
7. Does the result include area?
Yes. The result includes area, perimeter, heights, inradius, circumradius, side type, and angle type along with the solved angles.
8. Can I download the result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple printable result report.