Final answer:
The distance across the river can be calculated using trigonometry and is approximately 70 meters. If conversion to feet is required, the result is approximately 229.658 feet. None of the options provided match these results, so verification of the details or the measurement system used in the question is needed.
Step-by-step explanation:
To determine the distance across the river where the new bridge will be built, we should use trigonometry. From the information provided, the surveyor has created a right-angled triangle where one side (the baseline) is 100 m and the angle from the baseline to the tree across the river is 35°. We can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle.
The formula is tan(θ) = opposite/adjacent, so we rearrange this to find the distance across the river (opposite), which gives us opposite = adjacent * tan(θ). Therefore, the distance across the river is 100 m * tan(35°).
Calculating this, we get the distance across the river is approximately 70 meters. Since none of the options provided in the question exactly match this result, the student should verify the details or the question might be missing the correct answer, or handles a different measurement system like feet instead of meters.
If we are supposed to provide the answer in feet, we would need to convert the distance from meters to feet using the conversion factor 1 meter = 3.28084 feet. Multiplying 70 meters by this conversion factor gives us approximately 229.658 feet. Again we face the situation where the answer is not among the given options, therefore, a revision of the question and the provided options is recommended.