Calxsolver
Trigonometry

Law of Sines

The law of sines states that a/sin A = b/sin B = c/sin C for any triangle. Given two angles and the side opposite one of them, this solver finds the third angle by the 180° rule and then the two remaining sides.

Law of Sines

Solve a triangle from two angles and a side.

Try:
AnswerC = 65°, b = 15.0271, c = 14.0996
  1. GivenA = 40°, B = 75°, side a = 10
  2. Third angleC = 180° − A − B = 65°
  3. Law of sinesa / sin A = 10 / 0.642788 = 15.5572
  4. Side bb = (a/sin A)·sin B = 15.0271
  5. Side cc = (a/sin A)·sin C = 14.0996
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Worked examples

Law of sines: A = 30°, B = 60°, a = 10 Find the third angle and the two remaining sides with the law of sines.

Key terms

Sine In a right triangle, the ratio of the side opposite an angle to the hypotenuse.

Frequently asked questions

What is the AAS case?

AAS means Angle-Angle-Side: two angles and a non-included side. The third angle follows from A + B + C = 180°.

Does this handle the ambiguous SSA case?

No. SSA (two sides and a non-included angle) can have zero, one or two solutions; this tool covers the unambiguous AAS case.

Which side should I enter?

Enter side a, the side opposite angle A. The solver finds the rest from the sine ratio.

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