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Exercise 8: Cosine Rule & Similarity Transformation

Exercise 8: Cosine Rule & Similarity Transformation
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2017-06-14 14:45
TrigonometryMatrixTransformationGeometric Construction
This example demonstrates the application of the Cosine Rule to calculate triangle side lengths and angles, while showcasing geometric similarity through similarity transformations. Key math concepts include the Cosine Rule, geometric mean, similarity transformations, matrix applications, and curve sketching. GeoGebra commands and objects like Random, RandomElement, Textfield, TableText, and objects such as a, a_1, c, b, g are utilized in the construction. Suitable for high school mathematics education to understand the application of trigonometric functions in geometry and transformation properties.

GeoGebra Commands & Parameters

  1. Random(-10, 10) → a
  2. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → a_1
  3. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → c
  4. Random(-10, 10) → b
  5. Textfield(h) → InputBox1
  6. Random(-10, 10) → b_1
  7. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → c_1
  8. Random(-10, 10) → d_1
  9. Textfield(m) → InputBox2
  10. Textfield(f) → InputBox4
  11. TableText({{A1_1, B_1, C_1, D_1}, {-3, g(-3), h(-3), f(-3)}, {-2, g(-2), h(-2), f(-2)}, {-1, g(-1), h(-1), f(-1)}, {0, g(0), h(0), f(0)}, {1, g(1), h(1), f(1)}, {2, g(2), h(2), f(2)}, {3, g(3), h(3), f(3)}, {1, e, l, k}}, "|_") → text3_1
  12. Random(-10, 10) → d_2