To find the distance the plane traveled as it was taking off, we can use the relationship between the horizontal distance, the angle of takeoff, and the distance traveled.
Let's denote:
- \( d \) as the distance traveled by the plane,
- \( h \) as the horizontal distance covered, which is given as 950 m,
- \( \theta \) as the angle of takeoff, which is 78°.
The relationship can be expressed using the cosine of the angle:
\[ \cos(\theta) = \frac{\text{Horizontal Distance}}{\text{Total Distance}} \]
This means:
\[ \cos(78°) = \frac{950}{d} \]
Rearranging it gives:
\[ d = \frac{950}{\cos(78°)} \]
Now we can calculate \( \cos(78°) \):
\[ \cos(78°) \approx 0.2079 \]
Now substituting this into the equation for \( d \):
\[ d = \frac{950}{0.2079} \approx 4,573.19 \text{ m} \]
However, let's double-check the cosine calculation and solve again for verification:
Using \( \cos(78°) \approx 0.2079 \) gives:
\[ d \approx \frac{950}{0.2079} \approx 4,573.19 \text{ m} \]
Thus, the calculated distance of approximately 4,573.19 m does not match any of the options you provided. Since you provided specific options, let's check which one is closest:
The nearest value from the options given (assuming the angle is precisely taken into account) is:
• 4,569.25 m.
So, that would be the answer if you're looking to select from the provided rounded choices.
1 answer