About This Tool
The ASA (Angle-Side-Angle) case is when you know two angles of a triangle and the side between them (the included side). This configuration uniquely determines the triangle โ there's exactly one triangle that fits.
First, the calculator finds the third angle (since angles sum to 180ยฐ). Then it uses the Law of Sines to find the remaining two sides. You get all three sides, all three angles, area, perimeter, heights, and a scaled diagram.
ASA problems are common in surveying, navigation, and physics where you can measure angles from two observation points with a known distance between them.
How to Use
1. Enter the two known angles
2. Enter the side that connects them (the included side)
3. For example: if you know angles A and B, enter side c (which is between vertices A and B)
4. The third angle is calculated as 180ยฐ - A - B
5. The remaining sides are found using Law of Sines
6. Toggle between degrees and radians as needed
7. View the step-by-step solution and visual diagram
Formula
Third angle:
C = 180ยฐ - A - B
Law of Sines (to find remaining sides):
a/sin(A) = b/sin(B) = c/sin(C)
If you know side c:
a = c ยท sin(A) / sin(C)
b = c ยท sin(B) / sin(C)
Area:
Area = ยฝ ยท cยฒ ยท sin(A) ยท sin(B) / sin(C)