Question

A swimming pool has a depth of 6 ft at the shallow end and 12 ft at the deep end. The bottom of the pool slopes downward at an angle of 5.1 degrees. How long is the pool?

Answer 1

SeFinal answer:

To find the length of the swimming pool, we can use trigonometry. Using the given depth difference and angle, we can calculate the length of the pool as approximately 65.68 ft.

Step-by-step explanation:

To find the length of the swimming pool, we can use trigonometry.

Let's name the length of the pool as 'L'.

Using the given information, we can create a right triangle where the opposite side is the depth difference between the shallow and deep end (12 ft - 6 ft = 6 ft) and the adjacent side is the length of the pool. The angle between the hypotenuse and the adjacent side is 5.1 degrees.

Using the tangent function, we have:

tan(5.1 degrees) = (6 ft) / L

Solving for L, we get:

L = (6 ft) / tan(5.1 degrees)

Plugging in the values and calculating, we find that the length of the pool is approximately 65.68 ft.