To find the distance the plane traveled as it was taking off, we can use the horizontal distance and the angle of takeoff. We can find the actual distance traveled by using the cosine of the angle.
Given:
- Horizontal distance \( d_h = 950 \) m
- Angle of takeoff \( \theta = 78° \)
Using the relationship:
\[ d_h = d \cdot \cos(\theta) \]
where \( d \) is the actual distance traveled by the plane, we can rearrange this equation to find \( d \):
\[ d = \frac{d_h}{\cos(\theta)} \]
Now, we will calculate \( d \):
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Calculate \( \cos(78°) \):
- Using a calculator, \( \cos(78°) \approx 0.2079 \) (rounded to four decimal places).
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Substitute into the equation: \[ d = \frac{950}{\cos(78°)} \approx \frac{950}{0.2079} \approx 4,573.39 \text{ m} \]
It seems the calculated value of 4,573.39 m does not exactly match any of the provided options. Let's round down slightly for practical purposes.
We see that the closest option is 4,569.25 m, so the answer is:
4,569.25 m