Law of Sines Calculator

Use the law of sines to find missing sides and angles when you know a side and the angle opposite it.

Side a	10
Angle A (°)	40
Angle B (°)	60
Side b (instead of angle B, for SSA)

Side a

Angle A (°)

Angle B (°)

Side b (instead of angle B, for SSA)

Area

66.34139482

This is a scalene, acute triangle with sides 10, 13.472964, 15.320889 and angles 40°, 60°, 80°.

Sides a, b, c: 10, 13.472964, 15.320889
Angles A, B, C: 40°, 60°, 80°
Perimeter: 38.79385242
Heights to a, b, c: 13.268279, 9.848078, 8.660254
Inradius / circumradius: 3.420201 / 7.778619

Your triangle

About the Law of Sines Calculator

In any triangle, each side divided by the sine of its opposite angle gives the same number (the diameter of the circumscribed circle). Use it when you know two angles and a side, or two sides and an angle opposite one of them.

The formula

a / sin A = b / sin B = c / sin C = 2R

R: circumradius

Worked example

a = 10, A = 40°, B = 60°

C = 80°
b = 10 × sin 60° ÷ sin 40° ≈ 13.473

Questions people ask

When should I use the law of cosines instead?

When you know three sides, or two sides and the angle between them.

What is the ambiguous case?

With two sides and an angle not between them (SSA), sin B = b sin A / a has two solutions, B and 180° − B. When both leave room for the third angle, two different triangles fit, and the calculator solves both.