Final answer:
To determine the width of the river, the tangent function in trigonometry is used. The angle given is 35°, and by using the tangent of this angle and multiplying by the baseline distance of 100 m and then converting to feet, the river width is found to be approximately 229.7 ft. However, there seems to be an issue as this result does not match the provided answer choices.
Step-by-step explanation:
In the given problem, the student is presented with a scenario involving trigonometry, specifically right-angled triangles, where measurements from a riverbank are used to calculate the width of the river. We are told that the surveyor walks 100 m along the river and then uses an angle of 35° to sight a tree on the opposite bank.
To find the width of the river x, one can use the tangent function from trigonometry, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. We have tangent of the angle (θ) = opposite side (x) / adjacent side (100 m). In this case, the tangent of 35° equals x / 100 m.
By calculating the tangent of 35° and multiplying by 100 m, we can find the value of x. Tangent (35°) is approximately 0.7002, so x = 0.7002 × 100 m, giving us x ≈ 70.02 m. However, to match the units in the student's question and the available answers, we convert meters to feet, using the unit conversion that 1 m = 3.281 ft, which gives us x ≈ 70.02 m × 3.281 ft/m ≈ 229.7 ft. However, this does not directly match the available answer choices (a) 18.7 ft, (b) 11.2 ft, or (c) 40.0 ft. Therefore, it appears there may be a unit discrepancy or error in the original text provided by the student.