Homework Help: Precalculus

Posted by Ms. Suzie on Monday, March 2, 2009 at 1:29pm.

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

Precalculus - Reiny, Monday, March 2, 2009 at 2:07pm
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 right-angled 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.

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