To find the horizontal distance \(d\) that a plane needs to fly to reach the ground while descending at a 12° angle, given its altitude of 1,000 feet, we can use trigonometry.
In this scenario, we can consider a right triangle where:
- The altitude (height) of the plane is the opposite side \(h = 1000\) feet.
- The angle of depression is \(12°\).
- The distance \(d\) is the adjacent side.
Using the tangent function, which relates the opposite side to the adjacent side in a right triangle:
\[ \tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}} \]
We can set up the equation:
\[ \tan(12°) = \frac{1000}{d} \]
To find \(d\), we rearrange the equation:
\[ d = \frac{1000}{\tan(12°)} \]
Next, we need to calculate \(\tan(12°)\). Using a calculator:
\[ \tan(12°) \approx 0.2126 \]
Substituting this value into the equation gives:
\[ d = \frac{1000}{0.2126} \approx 4706.27 \]
Rounding to the nearest foot, the distance the plane still needs to fly to reach the ground is:
\[ \boxed{4706} \text{ feet} \]