Calculadora da Lei dos Senos
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
a/sen(A) = b/sen(B) = c/sen(C)
About this calculator
The Law of Sines Calculator solves any triangle using the ratio between sides and sines of opposite angles. Given two sides and the angle opposite one of them (SSA case), it finds the angle opposite the other side. The formula is a/sin(A) = b/sin(B) = c/sin(C).
How it works: enter known values (side a, side b, angle A). The calculator isolates sin(B) = b * sin(A) / a and uses arc sine to get angle B. If the sine exceeds 1, no triangle exists; if less, there may be two solutions (acute or obtuse angle).
Use this tool in navigation, engineering, architecture, or physics problems involving non-right triangles. For example, find the distance between two inaccessible points or the height of a building using elevation angles.
Cautions: the SSA case can have zero, one, or two solutions. Check if the given side is longer than the triangle's altitude. Use degrees or radians as configured. The calculator assumes angles are in degrees.
Frequently asked questions
What is the Law of Sines?
It states that in any triangle, the ratio of a side to the sine of its opposite angle is constant.
What data do I need to use the calculator?
You need two sides and the angle opposite one of them. For example, sides a and b and angle A.
What does the SSA case mean?
SSA means side-side-angle: we know two sides and an angle not between them. It can yield zero, one, or two solutions.
Does the calculator show both possible solutions?
Yes, if two solutions exist (acute and obtuse angles), the calculator will display both.
Can I use radians instead of degrees?
Currently the calculator uses degrees. If you need radians, convert before entering.