Final answer:
Using trigonometry, we calculate the separate distances to each hiker from the lookout tower using the angles of depression and the height of the tower. Subtracting the shorter distance from the longer one, we find that the hikers are approximately 12.24 feet apart, which does not match any of the given answer choices.
Step-by-step explanation:
To determine how far apart the hikers are from each other as seen by the person from the lookout tower, we can create two right triangles using the angles of depression and the height of the tower. Since the angles of depression are 4 and 6 degrees respectively, we can label these angles in our drawing where the lines of sight meet the ground. We will use trigonometry, specifically the tangent function, which relates the opposite side (distance from the base of the tower to the hiker) to the adjacent side (height of the tower).
The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Thus, for the first hiker, with an angle of depression of 4 degrees:
- tan(4°) = opposite/350 feet
The distance to the first hiker (opposite side) is distance1 = 350 * tan(4°). Similarly, for the second hiker, with an angle of depression of 6 degrees:
- tan(6°) = opposite/350 feet
The distance to the second hiker (opposite side) is distance2 = 350 * tan(6°). To find the distance between the two hikers, we subtract the smaller distance from the larger distance:
- distance_between_hikers = distance2 - distance1
Now we do the actual calculations:
- distance1 = 350 * tan(4°) ≈ 24.49 feet
- distance2 = 350 * tan(6°) ≈ 36.73 feet
- distance_between_hikers ≈ 36.73 - 24.49
The distance between the hikers is roughly 12.24 feet. However, none of the answer choices match this calculation, so we may need to review the process or verify the specifics of the question for any discrepancy.