Enter Triangle Values
Use the fields required by your selected method. Leave unrelated fields blank. Angles must be entered in degrees.
Example Data Table
| Method | Known values | Main formula | Expected use |
|---|---|---|---|
| SSS | a = 3, b = 4, c = 5 | Heron's formula and Law of Cosines | Find angles, area, and perimeter. |
| SAS | a = 7, b = 9, C = 50° | c² = a² + b² - 2ab cos(C) | Find the third side and all angles. |
| ASA/AAS | a = 10, A = 45°, B = 60° | a / sin(A) = b / sin(B) | Scale the full triangle from one side. |
| SSA | a = 8, b = 10, A = 30° | sin(B) = b sin(A) / a | Check one, two, or no solutions. |
Formula Used
Triangle inequality: a + b > c, a + c > b, and b + c > a.
Law of Cosines: c² = a² + b² - 2ab cos(C). It also finds angles when all three sides are known.
Law of Sines: a / sin(A) = b / sin(B) = c / sin(C). It is used for ASA, AAS, and SSA cases.
Heron's formula: s = (a + b + c) / 2 and Area = √[s(s-a)(s-b)(s-c)].
Extra measurements: heights use h = 2 × area / side. Inradius uses r = area / s. Circumradius uses R = abc / 4area.
How to Use This Calculator
- Select the triangle case that matches your known values.
- Enter side lengths in the same unit.
- Enter angles in degrees, not radians.
- Keep unrelated fields blank to avoid confusion.
- Press the calculate button and review the result above the form.
- Use the CSV or PDF button to save your result.
Understanding Triangle Side Calculations
Why Triangle Cases Matter
A triangle is simple in shape, but its missing values depend on the data you know. Three sides create an SSS case. Two sides with the angle between them create an SAS case. One side with two angles creates an ASA or AAS case. Two sides with a non-included angle create an SSA case. Each case needs a different formula.
This calculator handles those common cases in one place. It also checks whether a valid triangle can exist. That check is important. Some side lengths fail the triangle inequality. Some angle pairs exceed 180 degrees. Some SSA entries create no solution. Others create two different valid triangles.
What the Results Show
The result gives all three sides and all three angles. It also gives perimeter, semi-perimeter, and area. Advanced measurements are included too. You can review heights, medians, inradius, and circumradius. These values help with geometry study, drafting, construction checks, layout planning, and technical problem solving.
The side classification shows whether the triangle is equilateral, isosceles, or scalene. The angle classification shows whether it is acute, right, or obtuse. These labels help you understand the triangle beyond a single missing side.
Accuracy and Good Input
Use one unit system for every side. Do not mix feet with meters. Enter degrees for angles. Use the decimal setting to control rounding. Higher precision is useful for engineering style work. Lower precision is easier for classroom notes.
Practical Checks
Before using a result, check the source values. Measured sides can contain rounding error. Drawn angles can be approximate. A tiny change may alter a long side or a narrow angle. For field work, repeat the measurement. For school work, keep enough decimal places. For design work, record the unit and method. The notes beside each form field help prevent mixed cases. They also make the result easier to audit later.
The exported CSV is useful for spreadsheets. The PDF export is useful for reports, assignments, and saved records. Always compare results with the problem statement. Geometry formulas are reliable, but wrong input creates wrong output. Clean entries give clean results.
FAQs
1. What does side a mean?
Side a is the side opposite angle A. Side b is opposite angle B. Side c is opposite angle C. This naming follows standard triangle notation.
2. Can I calculate a triangle from three sides?
Yes. Choose the SSS method. Enter side a, side b, and side c. The calculator checks triangle inequality, then finds angles, area, perimeter, and extra measurements.
3. Which method should I use for two sides and one angle?
Use SAS when the angle is between the two known sides. Use SSA when the angle is not between the known sides. SSA may return two solutions.
4. Why can SSA have two answers?
SSA is ambiguous because the known side and angle can form two different triangle shapes. The calculator tests both possible angle B values and lists every valid solution.
5. Are angles entered in degrees?
Yes. Enter all angles in degrees. The calculator converts degrees internally for trigonometric functions and then reports final angles in degrees.
6. What is Heron's formula used for?
Heron's formula calculates area from three side lengths. It uses the semi-perimeter, so it is useful after the calculator has found all sides.
7. What does triangle inequality mean?
Triangle inequality means any two sides must add to more than the third side. If this rule fails, the sides cannot form a real triangle.
8. What can I export?
You can export the selected method, sides, angles, perimeter, area, and type. CSV works well for spreadsheets. PDF works well for printing or sharing.