ASA Triangle Calculator
Solve a triangle from the angle-side-angle (ASA) case: two angles and the side between them. Enter angle A, angle B, and the included side c, and the calculator finds the third angle, the remaining two sides (using the law of sines), and the area. It works for any valid triangle whose two given angles add to less than 180°.
Formula
C = 180° − A − B; a = c·sin(A)/sin(C); b = c·sin(B)/sin(C); Area = ½·a·b·sin(C)
- ASA means you know two angles and the side that lies between them. The third angle comes from the fact that all three angles sum to 180°.
- Once the third angle is known, the law of sines gives the remaining sides: each side divided by the sine of its opposite angle is constant.
- The included side c must be the one joining the vertices of angles A and B.
- Sides come out in the same length unit you enter for c; the area is in that unit squared.
Example: A = 50°, B = 60°, c = 7
Inputs
- Angle A (degrees): 50
- Angle B (degrees): 60
- Included Side c (between A and B): 7
The third angle is 180 − 50 − 60 = 70°. With c = 7, side a = 7·sin50°/sin70° ≈ 5.71 and side b = 7·sin60°/sin70° ≈ 6.45, giving an area of about 17.3 square units.
Frequently asked questions
What does ASA mean?
ASA stands for angle-side-angle: you know two angles of the triangle and the side that sits between them. That information uniquely determines the triangle.
How is the third angle found?
Because a triangle's angles always add up to 180°, the third angle is simply 180° − A − B.
How are the other two sides calculated?
By the law of sines: a = c·sin(A)/sin(C) and b = c·sin(B)/sin(C), where C is the third angle.
Why must A and B add to less than 180°?
If the two given angles summed to 180° or more, there would be nothing left for the third angle, so no triangle could exist.
What units should I use for the angles?
Enter all angles in degrees. The calculator converts them to radians internally for the trigonometric steps.