Question

A swimming pool is 30 meters long and 12 meters wide. The bottom of the pool is slanted so the water is 1.3 meters at the shallow end and 4 meters at the deep end. Find the angle of depression of the bottom of the pool.

Answer 1

in total the pool depth is 5.3

Answer 2

5.1427°

Explanation:

As we can observe in the first attached graph if we look the pool from the side we can identify a trapezoid which can be turned into a triangle (by drawing a paralell line to the 30m long side of the pool that goes from the shallowest side of the pool to the other side as we can see in the second attached graph )to be solved with trigonometric functions.

We are asked for the angle of depression (
`\alpha` in the second attached graph) which will go from the horizontal line to the deepest point of the pool. To find it we must use the trigonometric function that suits us which will be tan
`\alpha` because tangent is the ratio of the length of the side opposite to the angle (
`\alpha`) and the length of the side adjacent to the angle (
`\alpha`) like this:

`tan \alpha =(opposite)/(adjacent)`

Now we solve for
`\alpha`

`\alpha=tan^(-1)((2.7)/(30))=5.1427`°