Triangle Side Angle Calculator

Calculator Form

Example Data Table

Formula Used

Triangle validity: a + b > c, a + c > b, and b + c > a.

Angle A: A = cos^-1((b² + c² - a²) / (2bc)).

Angle B: B = cos^-1((a² + c² - b²) / (2ac)).

Angle C: C = 180 - A - B.

Perimeter: P = a + b + c.

Semi perimeter: s = P / 2.

Heron area: Area = √(s(s - a)(s - b)(s - c)).

Height: height to a side = 2 × Area / side.

Inradius: r = Area / s.

Circumradius: R = abc / (4 × Area).

Median to side a: m_a = 0.5√(2b² + 2c² - a²).

How To Use This Calculator

1. Enter the three side lengths of the triangle.
2. Use one matching unit for every side.
3. Add a project label if you need named exports.
4. Select how many decimal places should appear.
5. Press the calculate button.
6. Review angles, area, radii, heights, and type results.
7. Download the CSV file for spreadsheet records.
8. Download the PDF file for printable notes.

Article

Understanding Side Based Angle Calculation

A triangle becomes predictable when all three sides are known. This method is called SSS calculation. It does not need a height, a base angle, or a drawing scale. The calculator first checks that the three lengths can form a real triangle. The longest side must be shorter than the sum of the other two sides. Every side must also be greater than zero.

Why The Law Of Cosines Matters

After validation, the tool uses the Law of Cosines. Each angle is found by comparing one side with the two sides around it. The side opposite an angle has the strongest influence on that angle. A longer opposite side creates a larger angle. A shorter opposite side creates a smaller angle. This is why the largest side always faces the largest angle.

Extra Measurements For Better Review

The calculator also gives perimeter, semi perimeter, Heron area, heights, medians, inradius, and circumradius. These values help students, surveyors, makers, and teachers review the same triangle from many views. Heron area is useful because it uses only three sides. No separate height measurement is required. Heights are then derived from the area.

Triangle Type And Practical Use

Side type is reported as equilateral, isosceles, or scalene. Angle type is reported as acute, right, or obtuse. This helps catch mistakes quickly. For example, a nearly right triangle should show one angle near ninety degrees. A flat or impossible triangle is rejected before formulas run.

Using Results Carefully

Small rounding changes can appear when sides contain decimals. The calculator keeps internal values precise, then rounds only for display. Choose more decimal places when checking engineering, layout, or geometry homework. Use one consistent unit for all side inputs. The selected unit labels the results, but it does not convert mixed units. Always enter comparable side lengths before trusting the final angles.

Worked Example Insight

A strong example is a triangle with sides three, four, and five. The output should show a right triangle because the longest side squared equals the sum of the other two squared. Larger examples follow the same logic. Feet, meters, inches, and centimeters work when all entries share one unit. This supports quick comparison and careful review.

FAQs