Law of Sines Calculator
Use the law of sines to find a missing side. Given side a, angle A, and angle B, find side b.
Side B
17.3205
Formule
## Law of Sines ### Formula **a / sin(A) = b / sin(B) = c / sin(C)** This law relates the sides of any triangle to the sines of their opposite angles. ### Solving for Side b **b = a × sin(B) / sin(A)** ### When to Use Use the Law of Sines when you know: - Two angles and one side (AAS or ASA) - Two sides and an angle opposite one of them (SSA, but watch for the ambiguous case)
Exemple Résolu
Find side b: a = 10, angle A = 30°, angle B = 60°.
- 01b = 10 × sin(60°) / sin(30°)
- 02= 10 × 0.8660 / 0.5
- 03= 17.3205
- 04Angle C = 180 - 30 - 60 = 90°
Questions Fréquentes
What is the law of sines?
The law of sines states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C).
What is the ambiguous case?
When given two sides and a non-included angle (SSA), there may be zero, one, or two possible triangles. This is the ambiguous case of the law of sines.
When should I use law of sines vs law of cosines?
Use law of sines for AAS, ASA, or SSA problems. Use law of cosines for SAS or SSS problems.
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