Law Of Sines Calculator

Law of Sines Calculator

Solve a missing side length using the Law of Sines.

Last updated: June 2026 | By Patchworkr Team

Main Calculator

Resulting Side b
14.142136
b = a * sin(B) / sin(A) = 10 * sin(45 degrees) / sin(30 degrees)
Inputs are valid.

What is This?

The Law of Sines connects side lengths to the sines of their opposite angles in any triangle.

How to Use This Calculator

  1. Enter side a and two known angles.
  2. Make sure the angles sum to less than 180 degrees.
  3. Read the solved side b in the result panel.

Worked Example

a = 12, A = 40 degrees, B = 55 degrees
b = 12 * sin(55 degrees) / sin(40 degrees) = 14.993562

Frequently Asked Questions

Can I solve for another side?

Yes, but this calculator focuses on side b using the standard Law of Sines form.

Why are the angles restricted?

A triangle's interior angles must be positive and sum to less than 180 degrees.

Are decimals accepted?

Yes. Any finite real side length or angle in degrees is accepted.

What if the inputs do not form a triangle?

The calculator rejects angle pairs that leave no room for a third positive angle.

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