Triangle Side Angle Calculator

Enter Known Triangle Values

Use matching labels. Side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C.

Side a

Side b

Side c

Angle A in degrees

Angle B in degrees

Angle C in degrees

Side unit

Decimal places

Example Data Table

Case	Known Inputs	Method	Expected Use
SSS	a = 7, b = 9, c = 11	Law of cosines	Find all angles, area, and perimeter.
SAS	a = 10, b = 8, C = 50°	Law of cosines, then SSS	Find missing side and angles.
AAS	A = 45°, B = 65°, a = 12	Angle sum and law of sines	Scale the full triangle.
SSA	A = 35°, a = 9, b = 12	Law of sines	Check for one, two, or no triangles.

Formula Used

Angle sum: A + B + C = 180°.

Law of cosines: a² = b² + c² − 2bc cos(A). Similar forms are used for b and c.

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

Heron formula: Area = √[s(s − a)(s − b)(s − c)], where s = (a + b + c) / 2.

Perimeter: P = a + b + c.

Height: height to side a = 2 × area / a. The same pattern applies to b and c.

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 angle fields.
Keep side units consistent.
Select the preferred decimal precision.
Press the calculate button.
Review the result above the form.
Download CSV or PDF when needed.

Understand Any Triangle Faster

A triangle can look simple, yet its missing parts can confuse many users. This calculator helps you connect sides and angles with clear geometry rules. You can enter three sides, two sides with an included angle, two angles with one side, or an ambiguous side side angle case. The tool checks validity before it solves anything. That prevents impossible results and weak assumptions.

Why Side And Angle Solving Matters

Triangle solving is useful in surveying, design, navigation, school work, carpentry, mapping, and layout planning. A single missing side can affect a cut length. A single wrong angle can shift an entire drawing. The calculator shows the chosen method, so you can understand why each answer appears. It also reports area, perimeter, heights, inradius, circumradius, and triangle type.

Advanced Checks Included

The form accepts known sides a, b, and c. It also accepts angles A, B, and C in degrees. Each angle is opposite the matching side. The script detects SSS, SAS, ASA, AAS, and SSA patterns. When SSA creates two possible triangles, both solutions are shown. This is important because one side and one opposite angle may fit two valid shapes.

Better Reports For Reuse

After calculation, results appear above the form. You can download a CSV file for spreadsheet work. You can also create a PDF report for records, homework, or project notes. The chart gives a quick visual shape. It is not a drafting replacement, but it helps you inspect proportions. The example table gives sample entries for common cases.

Use Care With Real Projects

Rounded numbers can change final measurements. Use more decimal places for engineering or layout tasks. Check units before sharing results. The calculator keeps side units consistent. If you enter inches, all side outputs stay in inches, and area uses square inches. For safety critical work, verify values with approved plans or a qualified professional.

Keep Learning

Use the formula section as a learning guide. Compare given values with solved values. Then review the chart and table. This habit makes geometry practice easier. It also helps you catch data entry mistakes before exporting reports accurately for class, estimates, or planning.

FAQs

1. What values are required?

You need at least three known values. At least one must be a side. Common sets include three sides, two sides with an included angle, two angles with one side, or an SSA case.

2. What does side a mean?

Side a is opposite angle A. Side b is opposite angle B. Side c is opposite angle C. Use this matching system when entering mixed side and angle values.

3. Can this calculator solve SSA cases?

Yes. The calculator checks SSA inputs and can show two valid solutions when the ambiguous case occurs. It also reports when no valid triangle exists.

4. Why do my angles show a warning?

A warning appears when supplied angles or sides do not match the solved triangle closely. Check rounding, labels, and whether each angle is opposite the correct side.

5. Does the unit affect angles?

No. Units affect side, perimeter, height, radius, and area labels only. Angles are always entered and displayed in degrees.

6. What is the area formula?

When all sides are known, the calculator uses Heron formula. It first finds the semiperimeter, then calculates area from the three side lengths.

7. Can I export the result?

Yes. After calculation, use the CSV button for spreadsheet data. Use the PDF button to create a printable report with the main solved values.

8. Is this suitable for construction work?

It can help with planning and checking. For safety critical or regulated work, confirm results with approved drawings, field measurements, and a qualified professional.