Mathematics (4024)sin θ = Opposite / Hypotenuse cos θ = Adjacent / Hypotenuse tan θ = Opposite / Adjacent
Topic 8 of 8Cambridge O Levels
Trigonometry & Bearings
SOH CAH TOA, sine/cosine rules, bearings and angles of elevation
Right-angled triangles (SOH CAH TOA):
Finding sides: If angle = 30° and hypotenuse = 10: opposite = 10 × sin 30° = 5.
Finding angles: If opp = 3, hyp = 5: θ = sin⁻¹(3/5) = 36.9°.
Sine Rule (any triangle): a/sin A = b/sin B = c/sin C
Cosine Rule: a² = b² + c² - 2bc cos A
Bearings: Measured clockwise from North, always written as 3 figures. North = 000°, East = 090°, South = 180°, West = 270°.
Angles of elevation look UP from horizontal. Angles of depression look DOWN.
Key Points to Remember
- 1SOH CAH TOA for right-angled triangles
- 2Sine rule: a/sinA = b/sinB
- 3Cosine rule: a² = b² + c² - 2bc cosA
- 4Bearings: 3 figures, clockwise from North
Pakistan Example
Navigation and Bearings — Karachi to Islamabad Flight Path
A PIA flight from Karachi to Islamabad follows a bearing of approximately 020°. Pilots use trigonometry to calculate distances and headings. Similarly, Bykea delivery riders use angle calculations when navigating Karachi's grid-like DHA blocks.