Answer:

As an official tasked with determining the width of a river without actually measuring it, I would not use the same method as my predecessor. While using a stick and counting the number of steps taken to cross the river may provide an estimate, it is not an accurate or reliable method. Instead, I would employ a more scientific approach to determine the width of the river.

My plan to solve this challenge would involve using triangulation. Triangulation is a method used to calculate distances and angles by measuring the length of one side of a triangle and the angles between that side and the other two sides. In this case, I would use the opposite bank of the river as one point of the triangle, and two points on the same bank of the river as the other two points.

To begin, I would select two points on the same bank of the river, ideally at equal distances from the opposite bank. I would then measure the distance between these two points using a measuring tape or laser distance meter. Next, I would use a theodolite, which is a surveying instrument used to measure angles, to measure the angle between the line connecting the two points and the line connecting one of the points to the opposite bank of the river. I would repeat this process for the second point on the same bank of the river.

Using the data collected from these measurements, I would then calculate the width of the river using trigonometry. Specifically, I would use the formula: width = distance x tan(angle). By plugging in the measured distance and angle for each point, I would be able to calculate the width of the river at each point. I could then take the average of these two measurements to arrive at an estimate for the width of the river overall.

While this method may require more time and equipment than simply using a stick to count steps, it is a far more accurate and reliable method. By using triangulation, I would be able to account for any bends or curves in the river, as well as any changes in depth or width. This method would also allow me to account for any errors in my measurements, as I would be taking multiple measurements and averaging them out.

In conclusion, while the traditional method of using a stick and counting steps may provide a rough estimate of the width of a river, it is not a reliable or accurate method. Instead, I would use triangulation to determine the width of the river. By measuring the distance between two points on the same bank of the river and the angles between those points and the opposite bank, I could use trigonometry to calculate an estimate for the width of the river. While this method may require more time and equipment, it would provide a far more accurate and reliable estimate.