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Bearings (True and Compass)

Bearings (True and Compass)
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2013-11-20 21:01
AngleVectorTrigonometryCoordinate GeometryGeometric Construction
In collections GCSE Higher Ch8 Transformations & Constructions
This example demonstrates how to use GeoGebra to draw and calculate the relationship and conversion between true north bearings and compass bearings, involving core math concepts like angle measurement, vectors, geometric transformations, and coordinate systems. Key GeoGebra commands/objects used include Segment, Vector, and Angle for construction, suitable for high school mathematics teaching on applications in navigation and cartography.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Vector(A, C) → u
  3. Vector(B, D) → v
  4. Angle(A, B, D) → α
  5. Angle(B, A, C) → β
  6. Vector(B, E) → w
  7. Vector(A, F) → z
  8. Angle(E, B, A) → ζ
  9. Angle(A, B, E) → η
  10. Angle(D, B, A) → θ

AI Drawing Prompt Reference

Draw a coordinate system with two direction vectors u and v, and the true north bearings α and β formed by these vectors. Then, draw vectors w and z, which form angles ζ, η, and θ with vectors u and v respectively. Note that u and v represent directions in the geographic coordinate system, while w and z represent directions in the compass coordinate system.
The prompt above was compiled from the original drawing commands and is for reference only.