Nick wanted to determine the length of one blade of the windmill. He stood at a point on the ground 440 feet from the windmill's base. Using surveyor's tools, Nick measured the angle between the ground and the highest point reached by the top blade and found it was 38.8°. He also measured the angle between the ground and the lowest point of the top blade and found it was 30°.

To determine the length of one blade of the windmill, Nick used surveyor's tools and measured the angle between the ground and the highest point reached by the top blade (38.8°) and the angle between the ground and the lowest point of the top blade (30°).

In order to find the length of one blade of the windmill, Nick can use trigonometry and the information he has gathered. Let's consider the situation from a top-down view, where the windmill's base is the center, the ground point where Nick stands is a reference point, and the top blade of the windmill is positioned at an angle of 38.8° above the ground.

Since the top blade reaches the highest point, it forms a right angle with the ground. Thus, the angle between the top blade and the ground is 90° - 38.8° = 51.2°. Similarly, the angle between the lowest point of the top blade and the ground is 90° - 30° = 60°.

Now, Nick can use trigonometric ratios to calculate the length of one blade. Let's assume the length of one blade is represented by 'x'. Using the tangent function, we can set up the following equation:

tan(51.2°) = x / 440

By rearranging the equation, we can solve for 'x':

x = 440 * tan(51.2°)

Calculating the value of x using a scientific calculator, Nick will find the length of one blade of the windmill.

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