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