Law of Sines Calculator
Calculate triangle sides and angles using the Law of Sines with step-by-step solutions
📐 Law of Sines Calculator
AAS: ∠A = 30°, ∠C = 105°, side b = 12
Formula
a/sin(A) = b/sin(B) = c/sin(C)
Where:
- a, b, c =Triangle sides
- A, B, C =Angles opposite to sides a, b, c
- AAS =Angle-Angle-Side case
- ASA =Angle-Side-Angle case
- SSA =Side-Side-Angle (ambiguous case)
About Law of Sines
The Law of Sines relates the sides of a triangle to the sines of their opposite angles. It's essential for solving oblique triangles.
Triangle Cases:
- • AAS: Two angles and a non-included side (unique solution)
- • ASA: Two angles and the included side (unique solution)
- • SSA: Two sides and a non-included angle (ambiguous case)
Ambiguous Case (SSA):
- • Can have 0, 1, or 2 valid solutions
- • Occurs when given two sides and angle opposite smaller side
- • Both acute and obtuse angles may be valid
Applications:
- • Navigation and surveying
- • Engineering and construction
- • Astronomy and satellite positioning
- • Computer graphics and game development
- • Architecture and structural analysis
When to Use vs Law of Cosines:
- • Use Law of Sines for AAS, ASA, SSA cases
- • Use Law of Cosines for SAS, SSS cases
- • Law of Sines is simpler when angles are known
- • Law of Cosines avoids ambiguous cases