Saturday, April 25, 2015

444: Floorlamp

The floor lamp casts a shadow.
Straight line AB is drawn on a wide, spacious floor. A lamp is at a height of 8  m above point C, which is located on line AB.  Line CD is perpendicular to line AB.  A rectangular solid 5 m by 3 m by 4 m is on the floor as shown.  The box is 2  m from line AB and a meters from line CD. Assume the lamp is a point source and will cast a perfect shadow. Given that the rectangular solid casts a shadow with area 90  m², determine the distance a (in meters).

  • Does the 2m distance from the wall matter to the shape of the shadow?
  • How does the distance a change the area of the shadow?
  • What shape is that shadow on the floor? 
  • Are the edges of the shadow guaranteed to parallel with the edges of the box?
  • How far away is that box from the light? 
It's another Five Triangles puzzle

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