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Tangent of an Acute Angle

Tangent of an Acute Angle
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2023-03-14 03:41
AngleTrigonometryCoordinate GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates the construction of the tangent line to an acute angle α and its related geometric properties. It involves core math concepts like acute angles, tangent functions, geometric constructions, vectors, and coordinate geometry. Key GeoGebra commands used include Intersect, Point, Ray, Rotate, OrthogonalLine, Polygon, and Angle. Suitable for high school students learning about the geometric definition and properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Ray(A, B) → a
  4. Rotate(B, α, A) → C
  5. Ray(A, C) → b
  6. Point(a) → D
  7. OrthogonalLine(D, a) → c
  8. Intersect(c, b) → E
  9. Polygon(A, D, E) → P, c_a, c_o, h
  10. Angle(D, A, E) → β

AI Drawing Prompt Reference

Draw an acute angle α and construct its tangent line. First, draw the intersection point A of the x-axis and y-axis, then take a point B on the x-axis and draw a ray a through A and B. Rotate point B around A by angle α to get point C, and draw a ray b through A and C. Take a point D on ray a and draw a perpendicular line c to a through D. Line c intersects ray b at point E. Then, draw a triangle P with points A, D, and E. Finally, measure the size of angle DAE and label it as β.
The prompt above was compiled from the original drawing commands and is for reference only.