Enter Known Triangle Values
Example Data Table
| Case | Known Values | Use | Expected Pattern |
|---|---|---|---|
| SSS | a = 3, b = 4, c = 5 | Find all angles | Right triangle |
| SAS | a = 7, c = 5, B = 45° | Find missing side and angles | One triangle |
| AAS | A = 40°, B = 65°, a = 12 | Find sides b and c | One triangle |
| SSA | A = 35°, a = 8, b = 10 | Check ambiguous result | May show two triangles |
Formula Used
The calculator uses standard triangle relationships. It selects the best formula based on the values entered.
Angle Sum
A + B + C = 180°
Law of Sines
a / sin(A) = b / sin(B) = c / sin(C)
Law of Cosines
a² = b² + c² - 2bc cos(A)
b² = a² + c² - 2ac cos(B)
c² = a² + b² - 2ab cos(C)
Area and Radius Values
s = (a + b + c) / 2
Area = √(s(s - a)(s - b)(s - c))
Inradius = Area / s
Circumradius = abc / (4 × Area)
How to Use This Calculator
- Enter the triangle values you already know.
- Use side a opposite angle A, side b opposite angle B, and side c opposite angle C.
- Select degrees or radians for angle input.
- Choose the number of decimal places for the answer.
- Press Calculate to solve the triangle.
- Use CSV or PDF download to save the result.
Understanding Side and Angle Calculations
A triangle is small, yet it carries many checks. Each side has an opposite angle. When enough measurements are known, the missing parts can be solved. This calculator supports common triangle cases. It can handle three sides. It can handle two sides and an included angle. It can also solve two angles with one side. Ambiguous side angle cases are shown as separate possible triangles.
Why This Tool Helps
Manual work can be slow. One wrong sine or cosine step can change every later value. The calculator keeps the process structured. You enter the values you know. The script checks whether the data can form a valid triangle. It then solves the missing values. It also reports area, perimeter, semiperimeter, inradius, and circumradius. These extra values help with design, study, surveying, drafting, and geometry homework.
Measurement Rules
Use side a opposite angle A. Use side b opposite angle B. Use side c opposite angle C. This naming system matters. It helps the laws of sines and cosines work correctly. Angles may be entered in degrees or radians. The output is shown in degrees. Radian input is converted before solving. Sides can use any unit, as long as all side entries use the same unit.
Practical Accuracy
Triangle calculations often involve rounded values. A tiny difference is normal. The tool uses validation to catch impossible data. It rejects negative sides. It rejects invalid angles. It also warns when supplied extra values do not match the solved triangle. Increase decimals when you need a more exact report. Use fewer decimals for simple classroom checks.
Best Uses
This calculator is useful for construction sketches, map estimates, truss layouts, and math lessons. It is also helpful when checking old notes. The download options save the solved values. The example table gives starting cases. Always review your units before using results in real projects. For safety tasks, compare the result with a trusted drawing or professional method.
Common Mistakes to Avoid
Do not mix inches with centimeters. Do not place an angle beside the wrong side name. Do not assume a side angle case has only one answer. Check both possible results when the calculator lists them before choosing one.
FAQs
1. What does this calculator solve?
It solves missing triangle sides, missing angles, area, perimeter, semiperimeter, inradius, circumradius, and triangle type when enough valid measurements are entered.
2. How many values are required?
Most cases need three useful values. At least one side is needed when angles are used, because three angles alone do not define triangle size.
3. Can I enter all three sides?
Yes. Enter sides a, b, and c. The calculator checks the triangle inequality, then finds all angles with the law of cosines.
4. Can I use radians?
Yes. Select radians before calculating. The tool converts radian input to degrees internally and shows the solved angle values in degrees.
5. Why did I get two answers?
Some side-side-angle cases are ambiguous. The same known values can create two valid triangles. The calculator lists both when they exist.
6. Why is my triangle rejected?
The entered sides may not form a triangle, the angles may be invalid, or the extra supplied values may conflict with each other.
7. Do units matter?
Use one side unit throughout. You may use inches, meters, feet, or any other unit, but do not mix units in one calculation.
8. What is included in downloads?
The CSV and PDF files include solved sides, angles, area, perimeter, radius values, method used, and triangle classification.