9. a fish is 5.0 ft below the surface of a still pond. At what angle to the vertical must the fish look if it is to see a fisherman sleeping on the shore of the pond?

To determine the angle at which the fish must look to see the fisherman on the shore, we can use trigonometry. Let's consider the situation:

The fish is 5.0 ft below the surface of the pond, and we want to find the angle it needs to look to see the fisherman on the shore.

First, we'll draw a diagram to visualize the situation:

|
|
Fish | |
-----|H|-----|------ Pond Surface (level with the shore)
\ | | |
\ | 5.0 ft | |
\ | | |
\ | | |
\ | | |
\ | | |
\ | ---x---|--- Observer (Fish)

In the diagram, we have:
- The fish located at a depth of 5.0 ft below the surface of the pond.
- The observer (fish) looking towards the fisherman on the shore.
- The observer's line of sight from the fish to the fisherman is represented by the dotted line (x), which forms an angle with the vertical.

To find the angle, we can use the tangent function (tan) since we know the opposite side (5.0 ft) and the adjacent side (the horizontal distance between the observer and the fisherman).

Let's assume the horizontal distance between the fish and the fisherman is 20.0 ft:

Using the tangent function: tan(angle) = opposite/adjacent.
tan(angle) = 5.0 ft / 20.0 ft.

Now, we can solve for the angle by taking the inverse tangent (arctan) of both sides:
angle = arctan(5.0 ft / 20.0 ft).

Using a scientific calculator or an online calculator, you can find the inverse tangent of the ratio. The resulting angle will tell you at what angle the fish must look to see the fisherman on the shore.

Note: Make sure to use the same units for the sides (ft in this case) and convert if necessary.