Expert: Chen Min - 12/19/2008

Question
How far from the horizontal must a sheet of plywood 48
inches wide be rotated to fit through a doorway 30 inches
wide?

Hint : Draw a diagram.

I don't know where to begin with this one.  I've begun to
draw a diagram, but it is vague in what's it wants to be
labeled.  If you could go through the process and not just
supply the answer, that would be amazingly helpful.

Answer
It seems you have problem in constructing the math model.

You need to analyse it first: a plywood 48 inches wide into a doorway 30 inches wide--you are concerned with only the width of the two, so a two-dimensional frame will suffice.

Now, draw two vertical parallel lines as the doorway, the distance between them 30 inches. You don't need to specify the height as we are not concerned about it.

Then, you draw a horizontal line 48 inches wide as the plywood. Notice it's wider than the doorway, so you draw it in such a way that the protrudence at one side is 18 inches, so the other falls in the doorway.

Here it comes to the rotating part. You can make it clockwise or anti-clockwise, depending on where you made the pivot(the fixed side of the plywood). At one point the other side also falls into the doorway, this is the end point.

Now the question becomes: you have the two sides of an isosceles(a 48-inch plywood) and the distance from the peak to a foot on one side (30 inches) and you need to calculate the value of the peak angle.

Hope this helps.