Law of Sines Calculator
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Understanding the Law of Sines
The Law of Sines Formula
a/sin(A) = b/sin(B) = c/sin(C) = 2R
where R is the radius of the circumscribed circle
This law relates the lengths of the sides of a triangle to the sines of the corresponding angles.
When to Use the Law of Sines
ASA Case
Known: Two angles and one side
Find: Remaining side and angle
AAS Case
Known: Two angles and non-included side
Find: Remaining side and angle
SSA Case
Known: Two sides and non-included angle
Find: Remaining angles (may have two solutions)
The Ambiguous Case (SSA)
When using two sides and a non-included angle (SSA), there may be:
- No solution (impossible triangle)
- One solution (right triangle)
- Two solutions (ambiguous case)
This occurs because the same inputs could describe two different triangles.
Applications
Surveying
Used to find distances and heights of inaccessible points
Navigation
Essential in maritime and aerial navigation
Physics
Used in vector analysis and force problems