Final answer:
The width of the river can be calculated using trigonometry by applying the tangent function to the angle of 35° and the baseline of 100 meters established by the surveyor.
Step-by-step explanation:
Calculating the Width of a River
To calculate the width of the river using the surveyor's data, we need to apply trigonometry, specifically the tangent function. Given that the surveyor walked 100 meters along the river to establish a baseline and then measured an angle of 35° to the tree, we can set up the following equation using the tangent of the angle:
tangent(35°) = opposite/adjacent
Here, the opposite side is the width of the river, and the adjacent side is the baseline, which is 100 meters. We can then solve for the width (opposite side) as follows:
Width of the river = 100 meters × tangent(35°)
To solve this, we calculate the tangent of 35° and multiply it by 100 meters. The result will give us the river's width.
Note that to get an accurate measurement, the surveyor must ensure that the baseline is perpendicular to the flow of the river.