AAS Triangle Calculator — Solve Two Angles & Non-Included Side

About the AAS Triangle Calculator — Solve Two Angles & Non-Included Side

The AAS (Angle-Angle-Side) configuration provides two angles and a non-included side of a triangle. Because the three interior angles must sum to 180°, two angles immediately determine the third. With all three angles known and one side given, the Law of Sines uniquely pins down the remaining two sides: a/sin A = b/sin B = c/sin C.

AAS is one of the classic triangle congruence and solving conditions. Unlike SSA (which can produce the ambiguous case), AAS always yields exactly one triangle. Once all sides are known, you can compute the full suite of triangle properties — area (via Heron's formula or the ½ab sin C formula), perimeter, semi-perimeter, the three altitudes, the three medians, the inradius (radius of the inscribed circle), and the circumradius (radius of the circumscribed circle).

This calculator takes angle A, angle B, and side a (opposite angle A), computes all derived quantities, and shows visual bar comparisons of sides and angles. It also provides a reference table of triangle types and presets for common configurations like the 30-60-90 and 45-45-90 triangles.

When This Page Helps

Use this page when two angles and a non-included side are known and you want the full triangle from that data. It keeps the angle-sum step, Law of Sines solution, and the derived heights, medians, area, and radii together so the result can be checked as a full geometric object.

How to Use the Inputs

1. Enter angle A in degrees.
2. Enter angle B in degrees.
3. Enter side a (the side opposite angle A).
4. The calculator automatically finds angle C = 180° − A − B.
5. All sides are computed using the Law of Sines.
6. View area, perimeter, heights, medians, inradius, and circumradius.
7. Use presets to explore common triangle configurations.

Example Calculation

Tips & Best Practices

• AAS always produces exactly one triangle — no ambiguous case like SSA.
• If A + B ≥ 180°, no valid triangle exists.
• The longest side is always opposite the largest angle.
• The circumradius equals half the hypotenuse in a right triangle.
• Heights and medians coincide only in equilateral triangles.

When To Use This Calculator

Solve an AAS triangle given two angles and a non-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.

Frequently Asked Questions

• What is the difference between AAS and ASA?

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

• Can AAS give two possible triangles?

  No. AAS always gives exactly one triangle. The ambiguous case only arises with SSA (two sides and a non-included angle).

• How do I find the area from AAS?

  First solve for all sides using the Law of Sines, then use Heron's formula, or directly: Area = ½ × a × b × sin C.

• What is the inradius?

  The inradius is the radius of the largest circle that fits inside the triangle (the incircle). It equals the area divided by the semi-perimeter.

• What is the circumradius?

  The circumradius is the radius of the circle passing through all three vertices (the circumscribed circle). R = a / (2 sin A).

• Why does the Law of Sines work?

  The Law of Sines relates each side to the sine of its opposite angle: a/sin A = b/sin B = c/sin C = 2R, where R is the circumradius.