Expert: Steve Holleran - 10/1/2007

Question
Could you explain the following problem. I'm not sure how to start.

If the height of a rectangular prism is 10 inches and the sides of the square base each measure 5 inches, find a trigonometric equation to represent the angle formed by the diagonal of the prism with a diagonal of a base of the prism.  

Answer
Hi Tonia,

Well, I'm not exactly sure what is meant by "a trigonometric equation", but here's what we've got:

If the square base is 5 by 5, then the diagonal is 5*sqrt(2).

Then a right triangle is formed by the diagonal of the base and the diagonal of the prism and the altitude down to the base diagonal.  Call the angle you want x.

Then if you check a sketch, you can use the tangent function to write;

      tan x = 10 / 5 sqrt(2) = 2/sqrt(2) = sqrt(2)

Then if        tan x = sqrt(2), x = tan^-1 (sqrt(2)).

This is the only thing I can see that they want here.
Hope this helps.

Steve