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 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.
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!
Your approach is correct.
To find the depth of the deep end, you can use trigonometry and specifically the tangent function. Here's the step-by-step process:
1. Subtract the depth of the shallow end (3 feet) from the total length of the pool (50 feet): 50 - 3 = 47 feet. This gives you the horizontal distance between the shallow end and the deep end.
2. Set up a trigonometric equation using the tangent function: tan(12°) = depth of the deep end / 47.
3. Multiply both sides of the equation by 47 to isolate the depth of the deep end: tan(12°) * 47 = depth of the deep end.
4. Evaluate the expression on the right-hand side: tan(12°) * 47 ≈ 9.955 feet.
Therefore, the deep end of the swimming pool is approximately 9.955 feet deep. So your answer of 10 feet is very close and can be considered correct.