Question

1. what is the total height, in feet, of the flagpole?

Explanation:

Step1: Identify right - triangle relationships

We can consider the right - triangle formed by the flagpole, the ground, and the line from the top of the flagpole to the person's position. Let the height of the flagpole above the person's height be \(h\). Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 30\) (the hypotenuse) and \(a=3\) (the horizontal distance from the person to the base of the flagpole). So \(h=\sqrt{30^{2}-3^{2}}=\sqrt{900 - 9}=\sqrt{891}\approx29.85\).

Step2: Calculate total height of flagpole

The total height of the flagpole \(H\) is the sum of the height above the person and the person's height. The person's height is \(6\) ft. So \(H=6 + \sqrt{891}\approx6+29.85 = 35.85\) ft.

Answer:

Approximately \(35.85\) ft