Triangle Trigonometry Calculator

Enter Triangle Values

Use the selected method. Leave unused fields blank.

Solving method

Side a

Side b

Side c

Angle A in degrees

Angle B in degrees

Angle C in degrees

Side unit label

Decimal precision

Reset

Example Data Table

Method	Enter These Values	Sample Inputs	Main Output
SSS	a, b, c	a = 7, b = 9, c = 11	All angles, area, perimeter, heights
SAS	a, b, C	a = 8, b = 6, C = 50	Third side, missing angles, ratios
ASA or AAS	A, B, c	A = 45, B = 65, c = 12	Angle C, missing sides, area
Right triangle	c, A	c = 10, A = 30	Legs, angle B, trig ratios
SSA	a, b, A	a = 10, b = 12, A = 40	One or two valid triangles

Formula Used

Angle sum: A + B + C = 180 degrees.

Law of sines: a / sin(A) = b / sin(B) = c / sin(C).

Law of cosines: c² = a² + b² - 2ab cos(C). Similar forms solve sides a and b.

Heron's formula: s = (a + b + c) / 2, then area = √[s(s - a)(s - b)(s - c)].

Triangle area: area = 1/2 × a × b × sin(C), when two sides and their included angle are known.

Right triangle ratios: sin(A) = opposite / hypotenuse, cos(A) = adjacent / hypotenuse, tan(A) = opposite / adjacent.

How to Use This Calculator

Select the method that matches your known triangle information.
Enter the required sides and angles. Leave unused fields empty.
Use one consistent unit for every side length.
Enter all angles in degrees.
Choose the decimal precision for the final report.
Press the calculate button to view results above the form.
Download the CSV or PDF report when needed.

Understanding Triangle Trigonometry

Triangle trigonometry connects side lengths, angle measures, and shape properties. It helps students, builders, surveyors, designers, and engineers solve triangles when some values are known. This calculator supports common solving cases, including three sides, two sides with an included angle, two angles with a side, right triangle data, and ambiguous side side angle cases. Each result shows more than missing sides and angles. It also reports area, perimeter, heights, radii, and useful ratios. That makes the tool helpful for classroom checking and practical planning.

Why Accurate Setup Matters

Every triangle follows strict rules. The three angles must total one hundred eighty degrees. Side lengths must satisfy the triangle inequality. Opposite sides and opposite angles also grow together. A wrong value can create an impossible triangle, or it can create two possible triangles in an ambiguous case. The calculator checks these conditions before showing final values. This reduces guesswork and prevents misleading answers.

Main Calculation Ideas

The law of sines compares each side with the sine of its opposite angle. It is useful after one matching side and angle pair is known. The law of cosines handles three sides or two sides with the included angle. Heron's formula finds area from only side lengths. Standard sine, cosine, and tangent ratios explain right triangle relationships. These formulas work together to complete the triangle and confirm internal consistency.

Useful Output Details

The result panel gives rounded values for sides, angles, area, perimeter, semiperimeter, heights, inradius, and circumradius. It also shows trigonometric ratios for each solved angle. You can export the answer as a CSV file for spreadsheets. You can also create a simple report as a PDF. The example table gives sample inputs for each solving method, so users can test the form quickly.

Best Practice

Enter values carefully and choose the correct method. Keep units consistent across all side lengths. Use degrees for angle inputs. Review warnings when a triangle is impossible or ambiguous. For design, safety, or legal work, verify results with approved project standards.

Learning Benefit

This tool also encourages formula awareness. Users can compare methods, study ratio changes, and see how one missing value affects the full triangle. That supports stronger practice and faster daily review.

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 pattern helps formulas match each side with its related angle.

2. Which method should I choose?

Choose SSS for three sides. Choose SAS for two sides and the included angle. Choose ASA or AAS for two angles and one side. Choose right triangle when one angle is 90 degrees.

3. Can the SSA method give two answers?

Yes. SSA can be ambiguous. The same two sides and one non-included angle may create two valid triangles. The calculator shows both when both satisfy triangle rules.

4. Why are some fields unused?

Each solving method needs different known values. Extra fields are ignored, so you can leave them blank. The result depends only on the values required by the selected method.

5. What units can I use?

You can use any length unit, such as cm, m, inches, or feet. Keep all side inputs in the same unit, because mixed units create incorrect area and perimeter results.

6. Are angles entered in radians?

No. Enter all angles in degrees. The calculator converts degree values internally for sine, cosine, and tangent calculations, then displays final angles in degrees.

7. What does the circumradius mean?

The circumradius is the radius of the circle passing through all three triangle vertices. It is useful in geometry, design checks, and circle triangle relationship problems.

8. Why does the calculator reject my sides?

Your side lengths may fail the triangle inequality. The sum of any two sides must be greater than the third side. Otherwise, a real triangle cannot be formed.