To determine the angle of depression between the bird and the birdwatcher, we can use our understanding of trigonometric relationships within the right triangle formed by the bird, birdwatcher, and the vertical distance from the bird to the ground.
In this particular problem, the critical figures to consider are:
- The distance between the birdwatcher and the first bird: 29.7 feet
- The distance between the birdwatcher and the second bird: 42.1 feet
We are examining four possible angles of depression:
1. [tex]\(45.1^{\circ}\)[/tex]
2. [tex]\(44.9^{\circ}\)[/tex]
3. [tex]\(54.8^{\circ}\)[/tex]
4. [tex]\(35.2^{\circ}\)[/tex]
From the given information, we need to select the angle that corresponds correctly to the second bird's observed distance of 42.1 feet.
Given the multiple choices, through the process of selecting the correct angle that matches the calculated or understood distances correctly, the closest practical match is found. Matching this correctly, we find that:
The angle of depression between the second bird and the birdwatcher can be identified as:
[tex]\[ 54.8^{\circ} \][/tex]
Thus, the angle measure or angle of depression between the second bird and the birdwatcher is [tex]\(54.8^{\circ}\)[/tex].
