To determine the angle of depression from the bird (B) to the observer (O), we need to use the given distances and apply trigonometric principles.
1. Identify the given values:
- The hypotenuse (the line of sight from the observer to the base of the tower) is 9000 feet.
- The opposite side (the vertical distance from the bird to the top of the tower) is 6000 feet.
2. Understand the question context:
- The angle of depression from the bird to the observer is the same as the angle of elevation from the observer's point (O) to the bird's point (B).
3. Use the sine function to calculate the angle:
- In a right triangle, the ratio of the length of the opposite side to the hypotenuse side gives us the sine of the angle. Therefore, sin(angle) = opposite / hypotenuse.
4. Set up the equation:
- sin(angle) = 6000 / 9000
5. Calculate the ratio:
- sin(angle) = 0.6667
6. Find the angle using the inverse sine function:
- angle = sin^(-1)(0.6667)
7. Convert the angle from radians to degrees (since angles are often measured in degrees):
After following these steps, you find that the angle of depression is approximately [tex]\(41.81^\circ\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{41.81^\circ} \][/tex]
