Enter Triangle Values
Use any consistent side unit. Angles must be in degrees. Leave unknown values blank.
Example Data Table
| Case | Known Values | Suggested Inputs | Expected Use |
|---|---|---|---|
| AAS | A = 42°, B = 68°, a = 12 | Angle A, Angle B, Side a | Find all remaining sides and angle C. |
| ASA | A = 51°, C = 74°, b = 18 | Angle A, Angle C, Side b | Scale triangle using the sine rule. |
| SSA | A = 35°, a = 10, b = 12 | Angle A, Side a, Side b | Check for one or two possible triangles. |
| SAS | A = 60°, b = 8, c = 11 | Angle A, Side b, Side c | Find side a and area with sine. |
| SSS | a = 7, b = 9, c = 12 | Side a, Side b, Side c | Validate triangle and compute angles. |
Formula Used
Sine Rule
a / sin(A) = b / sin(B) = c / sin(C)
This rule works when a side and its opposite angle are known.
Angle Sum
A + B + C = 180°
The missing angle is found by subtracting known angles from 180 degrees.
Sine Area Formula
Area = 1/2 × b × c × sin(A)
Equivalent forms use the included angle between two known sides.
Height Formula
Height to a = 2 × Area / a
The same method applies to sides b and c.
How to Use This Calculator
- Enter any known sides and angles.
- Use side a opposite angle A, side b opposite angle B, and side c opposite angle C.
- Leave unknown boxes empty.
- Choose the decimal precision for the result.
- Press the calculate button.
- Review the result section shown above the form.
- Use CSV for spreadsheet records.
- Use PDF for printing or sharing.
Sine Triangle Calculator Guide
Why This Tool Matters
A sine triangle calculator helps when one side and matching angle are known. It also helps when two angles are known. The tool applies the sine rule to scale the whole triangle from one reliable pair. It can also check cases that start with three sides or two sides and one included angle.
Where It Helps
This page is useful for school work, layout checks, truss sketches, roof geometry, navigation examples, and simple design notes. You can enter sides in any consistent unit. You can enter angles in degrees. The result keeps the same side unit that you enter.
Correct Labeling
The calculator labels the triangle in standard form. Side a sits opposite angle A. Side b sits opposite angle B. Side c sits opposite angle C. This naming keeps the formula easy to audit. It also reduces mistakes when switching between known values.
Input Checks
Many triangle errors come from invalid data. Three angles must total 180 degrees. Each angle must be greater than zero. Three sides must pass the triangle inequality. In a valid triangle, no one side can be equal to or greater than the sum of the other two sides.
Ambiguous Cases
The sine rule is strongest when you know two angles and one side. It is also useful for AAS and ASA problems. SSA problems can create an ambiguous case. That means two different triangles may fit the same data. This calculator lists both possible solutions when they exist.
Area and Heights
Area is also included. When two sides and their included angle are known, the area equals one half times those sides times the sine of the included angle. Heights are derived from area. For example, height to side a equals twice the area divided by side a.
Graph and Export
Use the graph as a visual check, not as a construction drawing. The plotted triangle helps you see angle shape and side balance. It may not represent print scale. For records, download the CSV file. For sharing, use the PDF button. Review the formula steps before using results in exams, reports, or field planning. When values are rounded, tiny differences can appear. Increase precision for close comparisons. Always keep units consistent across every entered side before solving problems.
FAQs
1. What is a sine triangle calculator?
It is a triangle solver that uses the sine rule to find missing sides, missing angles, area, heights, and related measurements from known triangle values.
2. Which values should I enter?
Enter any valid combination, such as two angles and one side, three sides, two sides with an included angle, or an SSA sine pair.
3. What does side a mean?
Side a is opposite angle A. Side b is opposite angle B. Side c is opposite angle C. This standard naming helps prevent formula mistakes.
4. Why can SSA have two answers?
SSA can be ambiguous because one given side may swing into two possible triangle positions. The calculator lists both valid solutions when they exist.
5. Can I use inches or centimeters?
Yes. Use any side unit, but keep every side in the same unit. The calculator returns length, area, and height in matching units.
6. Why do my angles fail validation?
Triangle angles must be positive and total 180 degrees. If their sum is too high or too low, the triangle cannot exist.
7. Is the graph exact?
The graph is a visual guide. It helps show triangle shape and side balance, but it should not replace precise construction drawings.
8. What does the CSV export include?
The CSV file includes sides, angles, area, perimeter, heights, radius values, and sine ratio checks for each solved triangle.