To find the distance the plane still needs to fly to reach the ground, we can use trigonometry.
Given:
- Angle of depression = 12°
- Altitude of the plane = 1,000 feet
The distance the plane still needs to fly can be represented as the adjacent side of a right triangle, where:
- The altitude of the plane is the opposite side (1,000 feet).
- The angle of depression is the angle between the horizontal line and the line of descent.
Using the tangent function, which relates the opposite side to the adjacent side in a right triangle:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Where:
- \(\theta = 12°\)
- Opposite = 1,000 feet
We want to find the adjacent side (the distance the plane still needs to fly), which we can denote as \(d\):
\[ \tan(12°) = \frac{1000}{d} \]
Rearranging the equation gives:
\[ d = \frac{1000}{\tan(12°)} \]
Now, calculating \(\tan(12°)\):
\(\tan(12°) ≈ 0.2126\)
Now substituting the value of \(\tan(12°)\) into our equation:
\[ d = \frac{1000}{0.2126} \approx 4690.8 \text{ feet} \]
Rounding to the nearest foot:
\[ d \approx 4691 \text{ feet} \]
Thus, the distance the plane still needs to fly to reach the ground is approximately 4691 feet.