ASA Triangle Calculator
Two angles with the side between them determine a triangle completely. Enter them for the other two sides, the third angle and the area.
Angles in a triangle always add to 180°, so two of them give the third immediately.
How the asa triangle calculator works
Angles in a triangle always add to 180°, so two of them give the third immediately. The law of sines then scales the triangle to your known side: a ÷ sin A = b ÷ sin B = c ÷ sin C. The only requirement is that your two angles add to less than 180°, or nothing is left for the third.
Formula: a² = b² + c² − 2bc·cos A; a / sin A = b / sin B = c / sin C; area = ½ab·sin C
Worked examples
| Inputs | Area | Note |
|---|---|---|
| 40° and 60° with a side of 10 between | 28.2629 | the third angle is 80° |
| A 45-45-90 triangle | 25 | isosceles and right-angled |
| Surveying a 30-70 sighting | 149.092 | the classic surveying setup |
FAQFrequently asked questions
What does ASA mean?
Angle-Side-Angle: two angles and the side that lies between them. It fixes the triangle exactly.
How do I find the third angle?
Subtract the two you have from 180°. Every triangle's angles add to exactly that.
What is the law of sines?
Each side divided by the sine of its opposite angle gives the same number, so one known side scales the whole triangle.
Why is ASA used in surveying?
Because angles are easy to measure from two fixed points, and the distance between those points is the known side.
What if the side is not between the angles?
That is AAS, and it is solved the same way once you work out the third angle.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.