Cuboid 3D Trigonometry 02: Spatial Pythagorean and Vectors

①This example demonstrates how to apply trigonometry and the Pythagorean theorem in a three-dimensional cuboid to solve spatial angles and distances, and shows the use of vectors in solid geometry. ②Core mathematical concepts include right triangles in 3D space, the Pythagorean theorem, trigonometric functions (sine, cosine, tangent), spatial vectors, and properties of prisms. ③Construction highlights: using GeoGebra commands such as Intersect, Point, Polygon, PointIn, and Prism to construct the cuboid and its internal points, faces, and edges; defining multiple faces (e.g., faceABGF, faceBDHG) and edges (e.g., edgeAF, edgeBG) to build the 3D model, and using auxiliary polygons and segments for measurement and calculation. ④Suitable for high school or early college students learning solid geometry, trigonometry, and vectors, and for teachers demonstrating spatial geometric relationships in class or for student self-exploration.