Law of Sines Calculator Formula

Understand the math behind the law of sines calculator. Each variable explained with a worked example.

Use the Law of Sines Calculator

Formulas Used

Side B

side_b = side_a * sin(angle_b * pi / 180) / sin(angle_a * pi / 180)

Angle C

angle_c = 180 - angle_a - angle_b

Side C

side_c = side_a * sin((180 - angle_a - angle_b) * pi / 180) / sin(angle_a * pi / 180)

Variables

VariableDescriptionDefault
side_aSide a10
angle_aAngle A (degrees)(deg)30
angle_bAngle B (degrees)(deg)60

How It Works

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)

    • Worked Example

    Find side b: a = 10, angle A = 30°, angle B = 60°.

    side_a = 10angle_a = 30angle_b = 60
    1. 01b = 10 × sin(60°) / sin(30°)
    2. 02= 10 × 0.8660 / 0.5
    3. 03= 17.3205
    4. 04Angle C = 180 - 30 - 60 = 90°

    Ready to run the numbers?

    Open Law of Sines Calculator