HesapHanem

ASA Triangle Solver Calculator

Enter two angles and the side between them to solve the triangle.

How it is calculated

Enter two angles A and B in degrees and the side c that lies between them (the side joining the corners of A and B). The tool then works out:

C = 180° − A − B

a = c · sin A ÷ sin C and b = c · sin B ÷ sin C

Area = ½ · a · b · sin C

Side a is opposite angle A, side b opposite angle B. Sides and area are given to four decimals, angle C to two. All three inputs must be greater than zero and A + B must be less than 180°; otherwise there is no triangle and nothing is shown. The side keeps whatever unit you typed, and the area is in that unit squared.

Worked example

Take A = 40°, B = 60° and c = 10.

  1. C = 180 − 40 − 60 = 80°.
  2. a = 10 × sin 40° ÷ sin 80° = 10 × 0.6428 ÷ 0.9848 = 6.5270.
  3. b = 10 × sin 60° ÷ sin 80° = 10 × 0.8660 ÷ 0.9848 = 8.7939.
  4. Area = ½ × 6.5270 × 8.7939 × sin 80° = 28.2629.

The longest side, b, faces the largest of the two given angles, B, as it should.

Try this example →

Common mistakes

  • Entering a side that is not between the two angles. The tool assumes c joins the corners of A and B; if your known side is opposite one of the angles, that is the AAS case and c must be recomputed first with the law of sines.
  • Giving the angles in radians. Inputs are degrees, so 1.05 for 60° is read as just over one degree and the sides come out wildly wrong.
  • Using two angles that sum to 180° or more, for example 100° and 80°. No triangle exists then, and the tool returns nothing rather than a number.
  • Mixing up which side is a and which is b. Side a faces angle A, so swapping A and B also swaps a and b in the output.
  • Expecting a second solution. Unlike SSA, ASA always gives exactly one triangle, so there is no ambiguous case to check.

About this calculator

ASA (Angle-Side-Angle) is one of the classic triangle congruence cases: knowing two angles and the side between them is enough to fully determine a triangle. The solver first finds the third angle (angles sum to 180°), then applies the law of sines — a/sin(A) = b/sin(B) = c/sin(C) — to find the two unknown sides, and finally computes the area.

Solving triangles this way is a routine calculation in surveying, navigation, and engineering — for instance, triangulating a distant point's position from two known angles measured at either end of a known baseline, a technique that predates GPS and is still taught as the geometric foundation behind it.

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Comments (1)

  • Editorial team

    If your known side is not between the two known angles, you can still use this tool by relabelling. Say you know angles 40 and 60 and the side 6.527 opposite the 40 degree angle. The third angle is 80, and that side lies between the 60 and 80 degree corners. Enter 60, 80 and 6.527, and the outputs give about 8.79 and 10.00 for the sides opposite those two angles. Which surveying or layout problem are you solving?

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