Final answer:
The best estimate of the distance across the river, using trigonometry and the provided angle and baseline distance, is approximately 70 meters. This is obtained by using the tangent of the given angle (35°) and multiplying by the length of the baseline (100 m). None of the provided answer choices match this result.
Step-by-step explanation:
The problem provided is one of trigonometry, requiring us to calculate the width of a river based on certain given measurements. In the given scenario, a surveyor creates a 100 m baseline and identifies an angle of 35° from this baseline to a tree on the opposite side of the river. This setup forms a right triangle, where the river's width (d) is the side opposite the 35° angle, and the 100 m baseline is the adjacent side.
To find the width of the river, we can use the basic trigonometric function tangent, which is the ratio of the opposite side to the adjacent side in a right triangle ({tan(θ) = {opposite}/{adjacent}}). Thus, the equation becomes {tan(35°) = d/100}. We can solve for d by multiplying both sides by 100 m, giving us d = 100 {tan(35°)} m.
Using a calculator, we find that {tan(35°)} is approximately 0.7. Therefore, d = 100 {m} {0.7}, resulting in an estimated distance of 70 meters across the river. Since none of the provided choices A) 120 m, B) 130 m, C) 140 m, or D) 150 m match this result, it is likely there has been an error in the options given. The best estimate based on our calculations is 70 meters, which is not listed among the options.