Law of Sines Calculator
Law of Sines Calculator
The law of sines connects every side of a triangle to the sine of its opposite angle, in a ratio that stays constant throughout the whole triangle — and unlike basic right-triangle trigonometry, it works for any triangle, not just ones with a 90° angle. Enter angle A, its opposite side a, and angle B, and this calculator solves for the remaining angle and both remaining sides. Since a triangle's angles always add up to 180°, knowing just two angles and one side is enough information to solve the entire triangle.
- The law of sines states that a/sin(A) = b/sin(B) = c/sin(C) for any triangle, connecting each side to the sine of its opposite angle.
- Unlike right-triangle trigonometry, the law of sines works for any triangle, not just ones containing a 90° angle.
- Since a triangle's angles always sum to 180°, knowing any two angles instantly gives you the third, which is why this calculator only needs two angles and one side to solve the whole triangle.
How does the law of sines work?
Every side divided by the sine of its opposite angle gives the same ratio throughout a triangle — once you know that ratio from one side-angle pair, you can find any other side or angle.
If angle A = 30°, side a = 10, and angle B = 70°, what is side b?
b = a × sin(B) / sin(A) = 10 × sin(70°) / sin(30°) ≈ 18.79.
Law of Sines Calculator
The law of sines connects every side of a triangle to the sine of its opposite angle, in a ratio that stays constant throughout the whole triangle — and unlike basic right-triangle trigonometry, it works for any triangle, not just ones with a 90° angle. Enter angle A, its opposite side a, and angle B, and this calculator solves for the remaining angle and both remaining sides. Since a triangle's angles always add up to 180°, knowing just two angles and one side is enough information to solve the entire triangle.
- The law of sines states that a/sin(A) = b/sin(B) = c/sin(C) for any triangle, connecting each side to the sine of its opposite angle.
- Unlike right-triangle trigonometry, the law of sines works for any triangle, not just ones containing a 90° angle.
- Since a triangle's angles always sum to 180°, knowing any two angles instantly gives you the third, which is why this calculator only needs two angles and one side to solve the whole triangle.
How does the law of sines work?
Every side divided by the sine of its opposite angle gives the same ratio throughout a triangle — once you know that ratio from one side-angle pair, you can find any other side or angle.
If angle A = 30°, side a = 10, and angle B = 70°, what is side b?
b = a × sin(B) / sin(A) = 10 × sin(70°) / sin(30°) ≈ 18.79.