First, we must find the distance between Dimitri and the flagpole. As you can see in the figure attached, we draw a line with a 39° angle since to the point of sight (Which is called "A") to the bottom of the flagpole ("B"). We have that "A" is 5.8 feet above the ground, so we can find the distance AC:
Tan(α)=opposite leg/adjacent leg
The opposite leg is BC=5.8 feet, and the adjacent leg is the distance AC. So we have:
Tan(39°)=5.8/AC
AC=5.8/Tan(39°)
AC=7.16 feet
Let's find the height CD:
Tan(α)=opposite leg/adjacent leg
The opposite leg is CD and the adjacent leg is the distance AC=7.16 feet. Then:
Tan(39°)=7.16/CD
CD=Tan(39°)x7.16
CD=5.80 feet
Now we can calculate the height of top of the flagpole above the ground (BD):
BD=5.80 feet+5.80 feet
BD=11.6 feet
Rounded to the nearest foot:
BD=12.0 feet
How high is the top of the flagpole above the ground?
The answer is: 12.0 feet
