ASA Triangle Calculator
Calculate the missing angle, side lengths, perimeter, area, semiperimeter, and triangle radii based on two angles and the included side. ASA Triangle Calculator helps students, engineers, architects, and surveyors solve triangles accurately from known geometric measurements.
Highlights
- Solve ASA triangles using two known angles and the included side.
- Calculate the missing angle and remaining side lengths using the law of sines.
- Find perimeter, area, and semiperimeter with accurate triangle formulas.
- Determine circumradius, inradius, and altitude to the included side.
- Supports multiple angle and length units, including degrees, radians, metric, and imperial measurements.
Table of Contents
How ASA Triangle Calculator Works?
An ASA triangle is defined by two known angles, Angle A and Angle B, and the side c between them. The calculator first determines the missing angle using the angle-sum property of a triangle. The two supplied angles must have a combined value less than 180°.
After finding Angle C, the calculator uses the law of sines to determine the two unknown sides. Since side c is opposite Angle C, the side relationships are:
Therefore, the calculated sides are:
The perimeter and semiperimeter are calculated from the three side lengths:
The area can be found directly from the included side and the two known angles. This formula is equivalent to one-half the base multiplied by its altitude:
The altitude to side c, circumradius, and inradius are then calculated as follows:
| Output | Calculation basis |
|---|---|
| Missing Angle C | 180° − A − B |
| Side a | Law of sines |
| Side b | Law of sines |
| Perimeter | a + b + c |
| Area | c² sin(A) sin(B) ÷ [2 sin(C)] |
| Semiperimeter | Perimeter ÷ 2 |
| Circumradius | c ÷ [2 sin(C)] |
| Inradius | Area ÷ semiperimeter |
| Altitude to side c | 2 × Area ÷ c |
Angles may be entered and displayed in degrees, radians, or gons. The included side and length-based results support millimetres, centimetres, metres, kilometres, inches, feet, yards, and miles, while area results support the corresponding squared units.
Practical Use Cases
Students can use the calculator to check geometry and trigonometry exercises involving two angles and an included side, while reviewing how the angle-sum property and law of sines produce the remaining measurements.
Engineers can estimate the unknown sides, area, perimeter, radii, and altitude of triangular components when design measurements provide two angles and the connecting side.
Architects can apply the calculator to triangular floor plans, roof sections, façade elements, and other layouts where the included side and adjacent angular measurements are known.
Surveyors can solve a triangular survey configuration from two measured angles and the side between them, obtaining calculated side lengths, area, and the altitude to the measured side.
Accuracy and Limitations
The calculator uses standard double-precision trigonometric formulas, the triangle angle-sum property, the law of sines, and derived geometric relationships, so results are generally accurate to the displayed decimal precision for valid inputs. Angle A and Angle B must each be positive, the included side must be positive, and A + B must be less than 180°; otherwise no non-degenerate triangle exists. When the missing angle C is extremely close to 0°, the sine in the law-of-sines denominator becomes very small, so calculated sides, area-related values, and the circumradius can become highly sensitive to small measurement or rounding errors.
Quick Examples
Example #1: Standard Classroom Triangle
Solve a typical ASA triangle using two common angles and a measured included side.
Example #2: Construction Layout Triangle
Calculate triangle dimensions for a construction layout from angular measurements and a longer included side.
Example #3: Surveying Triangle
Use field surveying measurements to determine the missing angle and remaining triangle properties.
