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Solving Sides in Right Triangles

Solving Sides in Right Triangles
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2017-08-18 02:00
TriangleTrigonometryGeometric Construction
In collections Unit 9: Right Triangles and Trigonometry Unit 9: Right Triangles and Trigonometry
This example demonstrates how to solve for sides in right triangles using the Pythagorean theorem and trigonometric functions (sine, cosine, tangent). It involves interactive constructions with GeoGebra commands like Random, Distance, Polygon, Angle, RandomElement, If, Segment, and Intersect, suitable for high school geometry instruction and student practice in geometric calculations.

GeoGebra Commands & Parameters

  1. Random(5, 15) → da
  2. Distance(C, A) → distanceCD
  3. Distance(A, B) → distanceAB
  4. Distance(C, B) → distanceCB
  5. Polygon(A, B, C) → poly1, c, a_1, b
  6. Angle(B, A, C) → α
  7. Angle(C, B, A) → β
  8. RandomElement(sellist) → sel
  9. If(Element[sel, 1] ≟ 1, true, false) → sa
  10. If(Element[sel, 1] ≟ 2 ∨ Element[sel, 2] ≟ 2, true, false) → sb
  11. If(Element[sel, 1] ≟ 3 ∨ Element[sel, 2] ≟ 3, true, false) → sc
  12. If(Element[sel, 1] ≟ 4 ∨ Element[sel, 2] ≟ 4, true, false) → sd
  13. If(Element[sel, 2] ≟ 5, true, false) → se
  14. Segment(B, A) → d
  15. Segment(A, C) → e
  16. Segment(C, B) → f
  17. Intersect(a_1, f) → D
  18. Intersect(a_1, f) → E
  19. Intersect(e, poly1) → F, G
  20. Intersect(a_1, f) → H
  21. Intersect(d, a_1) → I

AI Drawing Prompt Reference

Draw a right triangle with randomly generated side lengths and label the three sides and two acute angles. Highlight one side or angle of the triangle in different colors based on a random selection, then draw the three sides and find some intersection points for further geometric constructions.
The prompt above was compiled from the original drawing commands and is for reference only.