55-Degree Right Triangle with Ratios

55-Degree Right Triangle with Ratios
Loading the math board and drawing, please wait…
2015-06-13 23:23
This example demonstrates a right triangle with a 55-degree angle, highlighting the ratios of its side lengths. Key math concepts include trigonometric functions (sine, cosine, tangent), properties of right triangles, and side length ratios. The construction uses GeoGebra commands such as Segment, OrthogonalLine, Rotate, Angle, Ray, Intersect, Distance, and Text. It is suitable for high school students to understand the application of trigonometry in right triangles and the calculation of side ratios, as well as for visualizing Riemann sums in calculus.

GeoGebra Commands & Parameters

  1. Segment(C, A) → adj
  2. OrthogonalLine(C, adj) → b
  3. Rotate(C, 305*°, A) → A'
  4. Angle(A', A, C) → α
  5. Ray(A, A') → c
  6. Intersect(b, c) → B
  7. Segment(C, B) → opp
  8. Segment(A, B) → hyp
  9. Angle(A, C, B) → β
  10. Distance(opp, hyp) → f
  11. Text(OppDivByHyp) → text2
  12. Text(AdjDivByHyp) → text1
  13. Text(OppDivByAdj) → text3