Law of Sines Calculator
Solve a triangle using the sine rule: a/sin A = b/sin B = c/sin C.
Inputs
Enter angle B to find side b.
Side b
10.724622
Side c
13.787309
Angle C
100.000000°
a/sin A ratio
14.000000
Step by step
Find angle C
C = 180° − 30° − 50°
= 100°
Common ratio
a/sin A = 7/sin(30°) = 7/0.5
= 14
Find side b
b = ratio × sin B = 14 × 0.766044
= 10.7246222
Find side c
c = ratio × sin C = 14 × 0.984808
= 13.78730854
How it works
The Law of Sines states that in any triangle, each side divided by the sine of its opposite angle is constant: a/sin A = b/sin B = c/sin C. It is used to solve triangles when you know AAS or ASA configurations.
Formula
Law of Sines
a / sin A = b / sin B = c / sin C
- a
- Side opposite angle A
- b
- Side opposite angle B
- c
- Side opposite angle C
Frequently Asked Questions
When do you use Law of Sines vs Law of Cosines?
Use Law of Sines when you know a side and its opposite angle plus one other measurement (AAS, ASA). Use Law of Cosines for SSS or SAS configurations.
What is the ambiguous case?
When given two sides and an angle opposite one (SSA), the Law of Sines may yield 0, 1, or 2 valid triangles because arcsin can have two solutions.