Final answer:
The width of the river, KH, can be calculated using trigonometry, with the formula involving the tangent of the given angle, resulting in a width of approximately 70.0 meters.
Step-by-step explanation:
To calculate the width of the river, KH, we can use trigonometry. Given that the surveyor walks 100 m along the river to establish a baseline and then sights across to a tree with an angle of 35° from the baseline, we are dealing with a right-angled triangle where the baseline is the adjacent side to the given angle, and the width of the river is the opposite side.
Applying the tangent function:
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- tan(35°) = opposite/adjacent
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- tan(35°) = width of the river / 100 m
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- width of the river = 100 m × tan(35°)
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- width of the river ≈ 100 m × 0.7002
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- width of the river ≈ 70.02 m
One possible mistake could be not recognizing this as a trigonometry problem or not computing the tangent of 35° correctly. Finally, rounding to the nearest tenth, the width of the river KH is approximately 70.0 meters, which was not an option provided. The available options may contain a typo, or the calculation method might not match the question as written.
Given the discrepancy, an additional review of the question or clarification with the student might be necessary.