To find the distance the plane still needs to fly to reach the ground while descending at a 12° angle of depression from an altitude of 1,000 feet, we can use trigonometry. Specifically, we can use the tangent function, which relates the angle of depression to the opposite side (altitude) and the adjacent side (horizontal distance).
Given:
- Angle of depression (θ) = 12°
- Altitude (opposite side) = 1,000 feet
Using the tangent function:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Rearranging gives us:
\[ \text{adjacent} = \frac{\text{opposite}}{\tan(\theta)} \]
Substituting the known values:
\[ \text{adjacent} = \frac{1000}{\tan(12°)} \]
First, we'll calculate \(\tan(12°)\):
\[ \tan(12°) \approx 0.2126 \]
Now substituting this value into the equation:
\[ \text{adjacent} = \frac{1000}{0.2126} \approx 4691.3 \text{ feet} \]
So, the distance the plane still needs to fly (the horizontal leg of the triangle) is approximately 4691.3 feet. Rounding to the nearest foot gives:
\[ \text{Distance} \approx 4691 \text{ feet} \]
Thus, the plane still needs to fly approximately 4,691 feet to reach the ground.