Answer:
First, we need to find the length of the slope connecting the shallow end and the deep end. We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the slope and the bottom of the pool:
h = sqrt((12.5 - 9)² + 4.5²) = 6.08 feet
Next, we need to find the difference in depth between the shallow end and the deep end. We can use the tangent of the angle of depression to find this difference:
tan(16.5) = (4.5 - d) / 6.08
where d is the depth of the pool at the deep end. Solving for d, we get:
d = 4.5 - 6.08 * tan(16.5) = 2.24 feet
Therefore, the depth of the pool at the deep end is approximately 2.2 feet.