Trigonometry

Building a bunk bed requires a lot of calculations and manipulations of numbers. But it was mostly straight forward until I got to the ladder part. Then I had to take out my calculator and figure out the angles, what my piece of wood had to look like in order to make it square with the rest of the bunk bed. It was a great application of my sin, cos, and tan and pythagoras theorem from junior high school.

An engineer working on a combustion experiment needs to create a rectangular plate with evenly spaced holes for the gas to go through.  The plate needs to be 100 cm by 50 cm (to fit into the machine), and the holes must be staggered, 3 cm apart.  One way she thinks of doing is to have the holes drilled in one row, all 3 cm apart.  For the next row, she was thinking of shifting the holes over, so that the holes make the vertices of equilateral triangles, with the previous row.  Then this would continue for the next rows, until the plate is completely drilled with holes.  The object o