Precalculus
posted by Ms. Suzie on .
A swimming pool is 3 feet deep in the shallow end. The bottom of the pool has a steady downward drop of 12 degrees toward the deep end. If the pool is 50 feet long, how deep is the deep end.
So I said that first you would subtract three from 50, of course giving you 47, then, I said
tan12 = x/47
tan12 * 47 = x
x = about 10 feet
is this right

the length is 50 feet, it has nothing to do with the fact that the depth is 3 feet at the shallow end.
make a sketch, showing a side view of the pool and you will see the problem more clearly. Draw a line horizontally to show a rectangle 50 by 3 at the top and a rightangled triangle with a length of 50 and a width of x feet
then tan12 = x/50
x = 50tan12 = 10.63 feet
x is the "additional" depth below the shallow end
so the deep end is 10.63 + 3 or
13.63 feet deep. 
The bottom of a swimming pool isn't a regular profile. The deep end is about 6 foot 6