Law of Sines Calculator
🔢 Enter known triangle parameters
💡 Fill in at least 3 fields, with at least one being a side
Law of Sines Calculator 📐
Solve any triangle using the law of sines. Find unknown sides and angles when you know at least 3 parameters (including at least one side).
📏 Law of Sines Formula
a/sin(A) = b/sin(B) = c/sin(C) = 2R
where a, b, c are the sides of the triangle, A, B, C are the opposite angles, and R is the radius of the circumscribed circle.
🎯 What you can find:
- ✅ Unknown sides from known angles and one side
- ✅ Unknown angles from known sides
- ✅ Circumradius of the triangle
- ✅ Area of the triangle
📋 Requirements:
You need to know at least 3 parameters, with at least one being a side. Examples: side + two angles, or two sides + one angle.
🔍 Applications:
Used in surveying, navigation, astronomy, and solving practical geometry problems in engineering and physics.
Frequently Asked Questions
What is the law of sines?
The law of sines establishes the relationship between the sides of a triangle and the sines of their opposite angles. All these ratios are equal and equal to twice the radius of the circumscribed circle.
When to use the law of sines?
Used for solving triangles in cases like AAS (angle-angle-side), ASA (angle-side-angle), and SSA (side-side-angle) when you have sufficient known parameters.
Can you solve a triangle knowing only the angles?
No, knowing only angles determines the shape but not the size. You need at least one side to fully solve the triangle.
What is the ambiguous case?
This occurs in SSA scenarios when the given side is shorter than the height. There might be two possible triangles, and the calculator will show both solutions.
What if the angles don't add up to 180°?
This indicates an error in input values, as the sum of angles in any triangle must equal 180 degrees.