Try drawing a diagram. If you "cut off" the right angle triangle at the bottom, you should be able to apply a trigonometric ratio.
I am having trouble understanding how to go about this word problem.
1)
A swimming pool is 40.0 feet long and 4.00 feet deep at one end. If it is 8.00 feet deep at the other end, find the total distance along the bottom.
your trouble in understanding what to do may be due to the fact that the question
has not stated that the bottom of the swimming pool is straight.
If it wasn't straight, you wouldn't have enough information.
Therefore, you can draw a right-angled triangle, with base=40ft and perpendicular height=8-4=4ft.
You then need to calculate the hypotenuse.
Pythagoras' theorem will do it,
but it appears you must work with an angle from the title of the question.
Therefore you'd need to use "inverse tan" to calculate an acute angle first.
Well by reading the question, you would not need to know the angle, just to find the distance along the bottom.
Using the pythagorus theorum,
we can work out c, which in this case is the distance along the bottom.
Can you find out the lengths of A and B for yourself?