ASA Triangle Calculator — Solve Two Angles & Included Side

Solve an ASA triangle given two angles and the included side. Compute all sides, area, perimeter, heights, medians, inradius, and circumradius.

First angle
°
The side between angles A and B
Second angle
°
Planning notes, formulas, and examples

About the ASA Triangle Calculator — Solve Two Angles & Included Side

The ASA (Angle-Side-Angle) condition provides two angles and the side between them (the included side). Since the three angles sum to 180°, knowing two immediately gives the third. With all three angles and one side known, the Law of Sines determines the remaining two sides: a/sin A = b/sin B = c/sin C. ASA is one of the four fundamental triangle congruence conditions (along with SSS, SAS, and AAS), and it always produces a unique triangle.

Once the triangle is fully determined, you can compute a wealth of properties. The area can come from Heron's formula or from the direct formula ½ab sin C. The three altitudes (heights) are each equal to 2 × Area divided by the base. The three medians follow from the formula mₐ = ½√(2b²+2c²−a²). The inradius — the radius of the inscribed circle tangent to all three sides — equals Area / s, where s is the semi-perimeter. The circumradius — the radius of the circumscribed circle through all three vertices — equals a/(2 sin A).

This calculator takes angle A, the included side c, and angle B, then solves the triangle completely. It displays visual bar charts comparing sides and angles, a heights-and-medians table, and an expandable reference of key triangle formulas.

When This Page Helps

Use this page when you need the full triangle from two angles and the included side. It keeps the angle sum, Law of Sines solution, and the derived measurements such as area, heights, medians, and radii together so the solved triangle is easy to verify.

How to Use the Inputs

  1. Enter angle A in degrees.
  2. Enter side c — the side between angle A and angle B.
  3. Enter angle B in degrees.
  4. The calculator computes angle C = 180° − A − B.
  5. Sides a and b are found via the Law of Sines.
  6. View area, perimeter, heights, medians, inradius, and circumradius.
  7. Click presets to explore common configurations.
  8. Expand the reference table for key triangle formulas.
Formula used
C = 180° − A − B a = c × sin A / sin C b = c × sin B / sin C Area = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2 Height hₐ = 2 × Area / a Median mₐ = ½√(2b²+2c²−a²) Inradius r = Area / s Circumradius R = a / (2 sin A)

Example Calculation

Result: A 30°-60°-90° triangle with included side c = 10

With A = 30°, B = 60°, and the included side c = 10, the third angle is 90°. The calculator then uses the Law of Sines to recover the other two sides and reports the full right-triangle geometry.

Tips & Best Practices

  • ASA always produces exactly one triangle — no ambiguous case.
  • If the two angles sum to 180° or more, no valid triangle exists.
  • An equilateral triangle is ASA with A = B = 60° and c = a = b.
  • The included side is always opposite the computed angle C.
  • You can verify results by checking that all three angles sum to 180° and the sides satisfy the Law of Sines.

When To Use This Calculator

Solve an ASA triangle given two angles and the included side. Compute all sides, area, perimeter, heights, medians, inradius, and circumradius. Use it when you need a repeatable calculation in the math / geometry category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Sources & Methodology

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Frequently Asked Questions

  • In ASA, the known side is between the two known angles (the included side). In AAS, the known side is not between the two angles. Both uniquely determine the triangle.

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