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Pythagorean Tunnel Depth Calculation

Pythagorean Tunnel Depth Calculation
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2014-06-03 16:17
TriangleTrigonometryGeometric Construction
In collections Pythagoras' Theorem
This example demonstrates how to calculate water depths in tunnels using the Pythagorean theorem. It involves core mathematical concepts such as right triangles and trigonometry. Using GeoGebra commands like Circle, Line, Intersect, Point, etc., a right triangle is constructed and its sides are calculated. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Line(B, C) → d
  3. Intersect(c, d, 1) → D
  4. Intersect(c, d, 2) → E
  5. Point(c) → F
  6. CircumcircleArc(D, F, E) → e
  7. CircumcircleSector(D, F, E) → f
  8. Polygon(D, E, A) → poly1, a_1, d_1, e_1
  9. Polygon(D, A, E) → poly2, e_2, d_2, a_2
  10. Point(c) → G
  11. Circle(A, G) → g
  12. Distance(D, E) → distanceDE
  13. Midpoint(D, E) → H
  14. Polygon(H, A, E) → poly3, e_3, h, a_3
  15. Distance(A, E) → distanceAE
  16. Angle(E, H, A) → α
  17. Polygon(I, J, K, L) → poly4, i_1, j_1, k, l
  18. Polygon(Q, R, S, T) → poly6, q, r, s, t
  19. Polygon(U, V, W, Z) → poly7, u, v, w, z

AI Drawing Prompt Reference

Draw a right triangle with point A as the right angle vertex and points D and E as the endpoints of the legs. Use the Pythagorean theorem to calculate the hypotenuse length and construct a circle with A as the center and DE as the diameter. Then, draw circles with D and E as centers and AD and AE as radii, respectively, and find their intersections with the hypotenuse. Finally, construct polygons using these intersection points and point A to demonstrate the properties of the right triangle.
The prompt above was compiled from the original drawing commands and is for reference only.