Question

A retangular in-ground pool is modeled by the prism below. The inside of the pool is 16 feet wide and 35 feet long. The pool has a

shallow end and a deep end, with a sloped floor connecting two ends. Without water, the shallow end is 9 feet long and 4.5 feet deep, and
the deep end of the pool is 12.5 feet long.

If the sloped floor has an angle of depression of 16.5 degrees, what is the depth of the pool at the deep end, to the nearest
tenth of a foot?

Answer 1

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.