Dmitri is looking up at the top of a flag pole. his line of sight is forming a 39° angle with the ground. his eyes are 5.8 feet above the ground. how high is the top of the flagpole above the ground? round to the nearest foot

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

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