A swimming pool is 3 ft deep in the shallow end the bottom of the pool has a steady downward drop of 12 degrees if the pool is 50 feet long how deep is the deepest end?

Y1 = 3Ft.

sin12 = Y2/50.
Y2 = 50*sin12 = 10.4 Ft.

Y = Y1 + Y2 = 3 + 10.4 = 13.4 Ft. = Depth of pool.

To determine the depth of the deepest end of the swimming pool, we can use trigonometry.

First, let's define some variables:
- D: Depth of the deepest end (in feet)
- A: Angle of the downward drop (in degrees)
- L: Length of the pool (in feet, given as 50 ft)
- S: Depth of the shallow end (in feet, given as 3 ft)

In this scenario, we have a right triangle formed by the shallow end (3 ft), the downward drop (12 degrees), and the depth of the deepest end (D).

We can use the tangent function to find the depth of the deepest end:
tan(A) = opposite / adjacent
tan(A) = (D - S) / L

Rearranging the equation to solve for D:
(D - S) = L * tan(A)
D = L * tan(A) + S

Now, let's substitute the given values into the equation:
A = 12 degrees
L = 50 ft
S = 3 ft

D = 50 * tan(12) + 3

Calculating this equation, we find:
D ≈ 9.42

Therefore, the depth of the deepest end of the swimming pool is approximately 9.42 feet.

To determine the depth of the deepest end of the swimming pool, we need to use trigonometry to calculate the change in depth caused by the downward drop.

First, let's define the angles and sides involved:

- The angle of the downward drop is given as 12 degrees.
- The length of the pool is given as 50 feet.

Now, we can use the trigonometric function tangent (tan) to calculate the change in depth caused by the angle.

The formula for calculating the change in depth is:

Change in depth = tan(angle) x length of the pool

Substituting the given values:

Change in depth = tan(12 degrees) x 50 feet

To solve this equation, we need to know the value of tan(12 degrees). We can use a calculator or a table that provides the trigonometric values for various angles.

Using a calculator or table, we find that tan(12 degrees) is approximately 0.21256.

Now, we can substitute this value back into the equation:

Change in depth = 0.21256 x 50 feet

Calculating this expression:

Change in depth = 10.628 feet

Therefore, the deepest end of the swimming pool is 10.628 feet deep.