Law of Sines Calculator – Two Angles and One Side
Solve a triangle from angles A, B and side a opposite A.
Formula
C = 180° − A − B; b = a sin B/sin A; c = a sin C/sin A.
Side a opposite A: 5 m · Angle A: 30 ° · Angle B: 60 ° · Side b opposite B ≈ (5 m)×sin((60 ° × 0.01745329252 rad/°))÷sin((30 ° × 0.01745329252 rad/°)) · Side c opposite C ≈ (5 m)×sin(pi-((30 ° × 0.01745329252 rad/°)+(60 ° × 0.01745329252 rad/°)))÷sin((30 ° × 0.01745329252 rad/°)) · Remaining angle C ≈ (pi-((30 ° × 0.01745329252 rad/°)+(60 ° × 0.01745329252 rad/°)))×180÷pi
How to use
- Enter side a and its opposite angle A.
- Enter angle B; A + B must be less than 180°.
- Read sides b, c in meters and angle C in degrees.
Examples
- a = 5 m, A = 30°, B = 90° gives b = 10 m.
Frequently asked questions
Which side must I enter?
Side a must be opposite angle A.
What if the angles sum to 180° or more?
These inputs are rejected. An angle within 10⁻¹² rad of degeneracy is also rejected for numerical stability.
Does this solve the ambiguous SSA case?
No. It requires two known angles, which determine the third.
Sources
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