To find the angle of depression from the bird (B) to the observer (O), we first identify the right triangle formed by points O, T, and B.
In this scenario:
- The vertical leg of the triangle (OT) represents the height of the tower and equals 200 feet.
- The horizontal leg of the triangle (BO) represents the distance from the observer to the base of the tower, which is 900 feet.
Since we want to find the angle of depression from the bird to the observer, we first need to find the angle \(x\) at point B (between line TB and line BO).
To find \(x\), we can use the tangent function, which relates the angle to the opposite and adjacent sides of the triangle: \[ \tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{OT}{BO} = \frac{200}{900} \] Calculating this gives: \[ \tan(x) = \frac{200}{900} = \frac{2}{9} \]
Next, we take the arctangent to find the angle \(x\): \[ x = \tan^{-1}\left(\frac{2}{9}\right) \]
Calculating this using a calculator: \[ x \approx 12.52^\circ \]
Now, since you're looking for the angle of depression from the bird (which is above the observer), the angle of elevation from O to T would also be \(12.52^\circ\). Thus, the angle of depression from B to O is 12.52°.
Therefore, the angle of depression from the bird (B) to the observer (O) is: \[ \boxed{12.52^\circ} \]
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