Law Of Sines Calculator
Use the Law of Sines to find unknown sides and angles in a triangle given two angles and one side.
Result
Please check your inputs.
How to Use This Tool
Enter the two known angles (A and B) into the calculator. Make sure you use degree or radian mode as required.
Type in the length of one side (a, b, or c) that corresponds to one of the angles you entered.
Click the 'Calculate' button. The tool will automatically apply the Law of Sines to find the unknown side and the third angle.
Review the results: you'll see the missing angle (C) and the lengths of the other two sides.
Use the 'Reset' button to clear all fields and start a new calculation with different values.
What Is Law Of Sines Calculator?
The Law of Sines is a fundamental rule in trigonometry that relates the sides of any triangle to the sines of its opposite angles. It states that the ratio of a side length to the sine of its opposite angle is constant for all three sides. This tool makes it incredibly easy to solve for missing sides or angles when you know two angles and one side — perfect for homework, engineering, or navigation problems. Using the Law Of Sines Calculator saves you from manual calculations and reduces errors, letting you focus on interpreting the results instead of grinding through formulas.
Formula
a / sin(A) = b / sin(B) = c / sin(C) = 2R, where a, b, c are the sides of the triangle, and A, B, C are the angles opposite those sides respectively. R is the circumradius of the triangle. In plain English: the length of any side divided by the sine of its opposite angle gives the same number for all three pairs. If you know two angles, you automatically know the third (since they sum to 180°), and then you can use the formula to find any unknown side.
Tips for Best Results
📐 Always double-check that your angles sum to 180° — if they don't, you may have entered them incorrectly.
📏 Use degree mode unless you're working in radians. Mixing units is a common source of errors.
🔄 If you get a 'no solution' error, check that your given angle-side pair is valid (e.g., sin value > 1).
✏️ This tool works for any triangle shape — acute, obtuse, or right — so don't worry about special cases.
Frequently Asked Questions
Do I need to enter angles in degrees or radians?
By default, most Law of Sines calculators assume degrees. If your problem uses radians, switch the mode first. Otherwise, your results will be incorrect. Always check the unit setting before inputting values.
What if I only know one side and two angles?
That's exactly the scenario this tool handles! Enter the two angles and the side you know. The calculator will find the third angle automatically (since angles in a triangle sum to 180°) and then compute the other two sides using the Law of Sines.
Can the Law of Sines be used for right triangles?
Yes, absolutely. The Law of Sines works for any triangle, including right triangles. In a right triangle, the sine of the 90° angle is 1, which makes the formula even simpler but still valid. The calculator handles all cases without needing special treatment.