To find the distance the plane traveled during takeoff, we can use trigonometry. The horizontal distance covered is the adjacent side of a right triangle formed by the distance traveled (the hypotenuse) and the angle of elevation (78°).
Let \( d \) be the distance the plane traveled. The horizontal distance covered is given by:
\[ \text{Horizontal Distance} = d \cdot \cos(\theta) \]
Substituting the given values:
\[ 950 = d \cdot \cos(78°) \]
Now, we can solve for \( d \):
\[ d = \frac{950}{\cos(78°)} \]
Using \( \cos(78°) \):
\[ \cos(78°) \approx 0.2079 \]
Now substituting this value:
\[ d = \frac{950}{0.2079} \approx 4569.25 \text{ m} \]
So the distance the plane traveled as it was taking off is approximately 4,569.25 m.
The correct answer is:
4,569.25 m.