SAT Math: Special Right Triangles in 3D
14+ practice questions in Praczo
The concept, explained
- 1
Special right triangles (30-60-90 and 45-45-90) are sometimes hidden inside 3D shapes like cubes, prisms, or pyramids.
- 2
The diagonal across a square face is the hypotenuse of a 45-45-90 triangle (side * √2).
- 3
The MAIN diagonal going through the interior of a cube from one corner to the opposite creates a right triangle with the face diagonal and a vertical side.
- 4
The formula for the main diagonal of a rectangular prism is √(l² + w² + h²). For a cube, it simplifies to s√3.
- ✗ Confusing a face diagonal (across flat surface) with an interior body diagonal (through the space).
- ✗ Using the 2D Pythagorean theorem improperly on 3D coordinates.
SAT-style practice
What is the length of the interior diagonal bridging opposite corners of a cube with side length 4?
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