Solve the Triangle Calculator

Triangle Inputs

Side a

Side b

Side c

Angle A in degrees

Angle B in degrees

Angle C in degrees

Length unit label

Decimal precision

Example Data Table

Case	Known Values	Method	Expected Output
SSS	a = 7, b = 8, c = 9	Law of cosines	Angles, area, perimeter, heights
SAS	b = 10, c = 12, A = 45°	Cosine rule, then sine rule	All sides and angles
ASA	A = 55°, B = 65°, a = 14	Angle sum and sine rule	Scale based complete triangle
SSA	a = 8, b = 10, A = 40°	Ambiguous sine rule	One or two valid solutions

Formula Used

The calculator uses several formulas, depending on the known values.

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).
Heron's formula: area = √[s(s - a)(s - b)(s - c)].
Semiperimeter: s = (a + b + c) / 2.
Perimeter: P = a + b + c.
Altitude: hₐ = 2 × area / a.
Inradius: r = area / s.
Circumradius: R = abc / (4 × area).

How to Use This Calculator

Enter at least three known values.
Include at least one side length.
Use degrees for all angles.
Keep every side in the same length unit.
Leave unknown fields blank.
Select the decimal precision you need.
Press the solve button.
Review the result above the form.
Download the CSV or PDF report when needed.

Smart Triangle Solving

A triangle can be solved when enough trusted measurements are known. This calculator accepts sides, angles, or a careful mix of both. It follows standard geometry rules. It checks each answer before showing the final values. That makes the result useful for school work, layout planning, drawing checks, and quick field estimates.

What the Tool Finds

The tool can return all three sides, all three angles, area, perimeter, semiperimeter, inradius, circumradius, median lengths, altitude lengths, and angle bisectors. It also reports the triangle type. You can see whether the shape is acute, right, obtuse, equilateral, isosceles, or scalene. These details help you understand the shape, not just the missing numbers.

Why Validation Matters

Triangle solving needs validation. Three angles alone give only shape, not size. Two sides and a non included angle can create two possible triangles. This is called the ambiguous case. The calculator lists every valid solution when that happens. It also rejects impossible entries, such as sides that break the triangle inequality or angles that cannot total one hundred eighty degrees.

Practical Use Cases

Use this calculator when checking drawings, roof pitches, land sketches, truss parts, classroom problems, navigation examples, and craft templates. Enter the values you trust most. Leave unknown boxes blank. Review the solution notes before using a measurement in real work. Rounding can hide small differences, so increase decimal precision when the job needs tighter results.

Accuracy Tips

Use the same length unit for every side. Do not mix inches and feet without converting first. Angles should be entered in degrees. For best results, use measured values with enough decimals. If your inputs came from a rough sketch, treat the answer as an estimate. If your inputs came from a certified drawing, the result can be used for stronger checking. Always compare the shown formulas with your project requirement. Some jobs require local standards or professional review.

Reading the Results

The result panel appears above the form after submission. This keeps the answer easy to copy. Download the CSV for records. Use the PDF button for a printable report. The example table shows sample inputs, so you can test the layout before entering your own measurements with confidence and compare clearly.

FAQs

1. What values are needed to solve a triangle?

You need at least three known values. At least one value must be a side length. Three angles alone define shape only, so they cannot define the actual size.

2. Can the calculator solve SSS triangles?

Yes. Enter all three sides. The tool checks the triangle inequality, then uses the law of cosines to find all angles and related measurements.

3. Can it solve SAS triangles?

Yes. Enter two sides and the included angle. The calculator first finds the missing side with the law of cosines, then completes the remaining angles.

4. Why can SSA give two answers?

SSA can be ambiguous because one side and one non included angle may fit two different triangle shapes. The calculator lists every valid solution it finds.

5. What angle unit should I use?

Enter every angle in degrees. Do not enter radians. The formulas internally convert degrees when trigonometric calculations are performed.

6. Can I mix feet, inches, meters, or centimeters?

Use one length unit for all sides. Convert mixed units before entering values. The unit label only names the output and does not convert measurements.

7. Why did I get a validation message?

A validation message appears when the values cannot form a valid triangle. Check zero values, impossible side lengths, angle totals, or inconsistent extra entries.

8. What does the PDF button include?

The PDF button exports the visible result panel. It includes solved sides, angles, area, perimeter, radii, medians, altitudes, bisectors, and type notes.