Final answer:
The width of the river can be determined using the tangent function in trigonometry, by calculating the product of Tan(35°) and the baseline distance of 100 m.
Step-by-step explanation:
The question asked pertains to surveying, which involves measuring angles and distances to determine the position of points on the earth's surface. The directions given involve cardinal points (North, East, South, and West) and angles measured from these directions, which is a common practice in surveying and navigation.
To answer the student's inquiry about the width of the river: the surveyor creates a baseline of 100 m length and then measures an angle of 35° from this baseline to the tree across the river.
This scenario forms a right triangle with the river width as the opposite side to the angle, the baseline as the adjacent side, and the line of sight to the tree as the hypotenuse. We can use trigonometry, specifically the tangent function, to calculate the width:
Tan(35°) = Opposite/Adjacent
Opposite = Tan(35°) × Adjacent
Opposite = Tan(35°) × 100 m
After calculating the tangent of 35° and multiplying by 100 m, we get the width of the river.