Final answer:
The width of the river can be determined using trigonometry by applying the tangent function which relates the angle of sighting to the lengths of sides in a right-angled triangle. The formula used is opposite = adjacent * tan(35°), which gives an approximate width of 70.02 meters.
Step-by-step explanation:
The requirement for the establishment of survey items such as lines, boundaries, and corners is not provided by a specific act in the scenario given, instead, the question pertains to solving a practical surveying problem using trigonometry. The width of the river can be determined using trigonometric principles, specifically by applying the tangent function which relates the angle of sighting to the lengths of sides in a right-angled triangle. Here's how to solve it:
- Draw a right triangle where the base is 100 m along the river, the height is the unknown width of the river, and the hypotenuse is the line of sight from the surveyor to the tree.
- The angle given is 35° from the baseline to the tree.
- Using the tangent function: tan(35°) = opposite/adjacent.
- Rearrange the equation to find the width of the river (opposite side): opposite = adjacent * tan(35°).
- Since the adjacent side (baseline) is 100 m, multiply this by tan(35°).
- Using a calculator, tan(35°) ≈ 0.7002.
- Multiply 100 m by 0.7002 to get the width of the river.
- The width of the river is therefore approximately 70.02 m.