To solve this problem, we can use trigonometry. We can create a right triangle where:
- The altitude (height) of the plane is the opposite side (1000 feet).
- The distance the plane needs to fly to reach the ground is the adjacent side (which we'll calculate).
- The angle of depression is \(12^\circ\).
Using the tangent function, which relates the angle to the opposite and adjacent sides of a right triangle, we can express this relationship as:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case, we have:
\[ \tan(12^\circ) = \frac{1000}{d} \]
where \(d\) is the distance the plane still needs to fly. Rearranging the equation to solve for \(d\):
\[ d = \frac{1000}{\tan(12^\circ)} \]
Now, we will calculate \(\tan(12^\circ)\):
\[ \tan(12^\circ) \approx 0.2126 \quad (\text{using a calculator}) \]
Now substituting that into the equation for \(d\):
\[ d = \frac{1000}{0.2126} \approx 4691.25 \]
Rounding to the nearest foot, the distance the plane still needs to fly to reach the ground is:
\[ \boxed{4691 \text{ feet}} \]
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