MathPlotAI Logo MathPlotAI

Sine Rule (Part 3)

Sine Rule (Part 3)
Loading the math board and drawing, please wait…
2017-10-31 15:57
TriangleTrigonometryGeometric Construction
This example demonstrates the application of the Sine Rule in solving triangle problems, involving core mathematical concepts such as the Sine Rule, triangle similarity, angle measurement, and optimization problems. Construction highlights include using GeoGebra commands like Point, Segment, Rotate, Line, Angle, Circle, and objects like dist, A, B, AB, α, Hleft, Hright, etc. Suitable for high school mathematics teaching and geometric construction practice.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 10]) → B
  2. Segment(A, B) → AB
  3. Point(Circle[B, 4]) → Draw
  4. Rotate(B, 30°, A) → B'
  5. Line(A, B') → h
  6. Segment(A, Point[AB, dist]) → AB'
  7. Angle(B, A, B') → α
  8. Segment(Hleft, Point[Segment[Hleft, Hright], distH]) → h'
  9. Segment(A, B') → f
  10. Segment(B, Draw) → Radius
  11. Circle(B, 4) → Circ

AI Drawing Prompt Reference

Draw a triangle with one side of length 10 and another side of length 4. Then, at the vertex opposite the side of length 4, draw a circle with radius 4 that intersects the triangle's other side. Rotate this intersection point 30 degrees around the vertex to get a new point. Connect the original intersection point and the new point. From the vertex, draw a perpendicular line to the new line segment, marking the foot of the perpendicular. Finally, connect the foot of the perpendicular to the new point.
The prompt above was compiled from the original drawing commands and is for reference only.