Final answer:
The width of a river can be measured by a biologist using surveying techniques, where the surveyor establishes a baseline alongside the river, measures an angle across the river, and then calculates the width with trigonometry.
Step-by-step explanation:
To determine the width of a river, a biologist could utilize a method of surveying similar to the technique used by a surveyor in the provided example. The surveyor establishes a known baseline distance alongside the river and then measures the angle from the baseline to a fixed point across the river using a theodolite or similar device. In the example given, the surveyor walks 100 meters along the river bank to form the baseline and then measures an angle of 35° to a tree on the opposite bank. With this information, trigonometric principles, specifically the use of tangents in a right-angled triangle, can be applied to calculate the width of the river.
Using the formula tangent(angle) = opposite/adjacent, we can solve for the opposite side, which represents the river width. Here, the tangent of 35° multiplied by the baseline distance of 100 meters gives us the width of the river. The exact calculation would be tan(35°) × 100 m, which can be computed using a calculator to get the width in meters.