The angle of elevation to the top of a flagpole measured by a digital protractor is $57.1^{\circ}$ from a point on the ground 68 feet away from its base. Find the height of the flagpole.

Step 1 ：The problem involves a right triangle, where the angle of elevation is given, and the distance from the observer to the base of the flagpole is given. We can use the tangent of the angle of elevation, which is equal to the height of the flagpole divided by the distance from the observer to the base of the flagpole, to find the height of the flagpole.

Step 2 ：The formula for the tangent of an angle in a right triangle is: \( \tan(\theta) = \frac{{\text{{opposite side}}}}{{\text{{adjacent side}}}} \)

Step 3 ：In this case, the opposite side is the height of the flagpole (which we are trying to find), and the adjacent side is the distance from the observer to the base of the flagpole.

Step 4 ：So, we can rearrange the formula to solve for the height of the flagpole: \( \text{{height}} = \tan(\theta) \times \text{{distance}} \)

Step 5 ：We know that the angle of elevation \( \theta \) is 57.1 degrees, and the distance is 68 feet.

Step 6 ：We can plug these values into the formula to find the height of the flagpole.

Step 7 ：Note: The math functions expect angles to be in radians, not degrees. So, we need to convert the angle from degrees to radians before using the tan function. The conversion factor is \( \frac{\pi}{180} \).

Step 8 ：Final Answer: The height of the flagpole is approximately \( \boxed{105.11} \) feet.