Law of Sines Calculator
Enter two angles and a side below to instantly solve the rest of the triangle.
Enter angle A, angle B, and side a (opposite angle A)
The Law of Sines
a/sin(A) = b/sin(B) = c/sin(C). Once you know two angles, the third follows immediately since every triangle's angles add up to 180°.
Worked example
Angle A = 30°, angle B = 45°, side a = 10.
Angle C = 180 − 30 − 45 = 105°
b = 10 × sin(45°) / sin(30°) ≈ 14.14
c = 10 × sin(105°) / sin(30°) ≈ 19.32
Frequently Asked Questions
What is the Law of Sines?
For any triangle, a/sin(A) = b/sin(B) = c/sin(C), where each lowercase letter is a side and the uppercase letter across from it is the angle opposite that side. It lets you solve for unknown sides or angles in any triangle, not just right triangles.
When do you use the Law of Sines instead of the Law of Cosines?
Use the Law of Sines when you know two angles and a side (AAS or ASA), or two sides and a non-included angle (SSA). Use the Law of Cosines when you know three sides (SSS) or two sides and the included angle (SAS).
Does the Law of Sines work on right triangles?
Yes — it works on every triangle, right triangles included. For a right triangle specifically, the Pythagorean theorem is usually faster, but the Law of Sines still gives the same correct answer.
Related Calculators
- Sphere Calculator — Geometry & Trigonometry
- Cylinder Calculator — Geometry & Trigonometry
- Cone Calculator — Geometry & Trigonometry
- Triangle Area Calculator — Geometry & Trigonometry