Angles in Triangles (AYT)
Learning Time: 4-12 hours
Content: Angles in triangles are covered at a more advanced level in the AYT curriculum, including angle-side relationships, triangle inequalities, trigonometric relations (sine and cosine rules), and complex problems. This topic supports the transition to analytic and synthetic geometry. The current 2025 AYT curriculum also includes vectors and triangle angles in space.
- Angle-Side Relations:
- Sine Rule (a/sin A = b/sin B = c/sin C)
- Cosine Rule (a² = b² + c² – 2bc·cos A)
- Trigonometric Proofs
- Trigon Inequalities:
- Angle-Side Inequality
- Conditions for Triangle Formation
- Minimum and Maximum Angle Analysis
- Trigonometric Applications:
- Trigonometric Expressions of Angles
- Calculating the Area of a Triangle (1/2 ab sin C)
- Vector Angle Analysis
- Proof and Problem Solving:
- Complex Triangle Problems
- Geometric Proof Techniques
- Triangle Angles in Space
- Applications:
- Triangle Analysis in Engineering
- Navigation and Cartography
- Fundamentals of Space Geometry
- Affecting Factors:
- Side Lengths
- Angle Measurements
- Trigonometric Values
Course Features
- Lectures 0
- Quizzes 0
- Duration 5 hours
- Skill level Expert
- Language English
- Students 15
- Assessments Yes
