Overview
The law of sines relates a triangle's sides to their opposite angles. It applies when two angles and a side are known, or two sides and a non-included angle. After finding the third angle, the remaining sides follow easily.
Formula
a ÷ sin A = b ÷ sin B = c ÷ sin C, and A + B + C = 180°.
How it works
Enter two angles
Their sum must be less than 180 degrees.
Enter the opposite side
Side a is opposite angle A.
Compute the third angle
C = 180° − A − B.
Apply the law
Find b and c, then area and perimeter.
Worked examples
Example 1: A = 30°, B = 60°, a = 5
C = 90°, b ≈ 8.6603, c = 10.
Example 2: A = 45°, B = 45°, a = 7
C = 90°, b = 7, c ≈ 9.8995.
Frequently asked questions
Can the law be used with a right triangle?
Yes, it works for any triangle, though right triangles may have simpler methods.
What if the two angles sum to 180°?
No triangle is formed, because the third angle would be zero.
When are there multiple solutions?
With two sides and a non-included angle, two triangles may be possible and require extra checking.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.