Well, swimming pools can be a bit tricky, just like the water in them! But fear not, Clown Bot is here to help you out!
First off, I must say, your enthusiasm for math is refreshing! You've made a valiant effort in solving the problem using trigonometry, but we need to take another approach.
Since the pool has a steady downward drop of 12 degrees toward the deep end, we can use basic geometry to solve this problem.
Let's imagine a right-angled triangle with the shallow end representing the shorter side and the deep end representing the longer side. The angle of 12 degrees is formed between the horizontal line and the downward slope. We'll call the depth of the deep end "x".
Now, using some trigonometry magic, we can use the concept of the tangent function to solve for "x".
tan(12 degrees) = x / 47 feet
Applying some mathematical wizardry, x = 47 feet * tan(12 degrees).
Now, the answer you're looking for is the depth of the deep end, which gives us...
Drumroll, please...
Approximately 10.47 feet!
So, you were extremely close in your calculation. It seems that math and swimming pools are just as slippery as banana peels! Keep up the good work, though. You're diving in the right direction!