How this calculator works
An altitude shows that side length divided by the sine of the opposite angle has the same value for all three pairs. In AAS mode the third angle is fixed. In SSA mode, sine gives the same value for an acute angle and its supplement, so both candidates must be checked against the angle sum. Impossible data produce an error rather than a fabricated triangle.
Formula
a/sin A = b/sin B = c/sin C; C=180°-A-B. SSA candidates: B₁=arcsin(b sin A/a), B₂=180°-B₁; retain only A+B<180°.
Worked example
With a = 10 m, A = 30° and B = 60°, the other sides are b = 10√3 m and c = 20 m. With a = 10 m, b = 10√3 m and A = 30°, SSA gives B = 60° or 120° and c = 20 m or 10 m.
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Frequently asked questions
Why can SSA give two answers?
An acute angle and its supplement share the same sine. Both may leave a positive third angle.
Can I relabel the triangle?
Yes. Rename your known opposite side-angle pair as a and A. The geometry does not depend on the letter names.
Does a sine argument above one have an answer?
No real angle has sine greater than one. A ratio within eight machine epsilons of one is treated as one to absorb rounding at a right angle.