To find the distance the plane traveled during takeoff, we can use basic trigonometry. The horizontal distance covered (950 m) represents the adjacent side of a right triangle, where the distance traveled by the plane represents the hypotenuse. The angle of ascent is given as 78°.
Using the cosine function:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Here, \(\theta\) is 78°, the adjacent side is 950 m, and the hypotenuse is the distance we want to find, which we'll denote as \(d\).
Rearranging the cosine formula to solve for the hypotenuse:
\[ d = \frac{\text{adjacent}}{\cos(\theta)} \]
Substituting the known values:
\[ d = \frac{950 \text{ m}}{\cos(78°)} \]
Now, we need to calculate \(\cos(78°)\). Using a calculator:
\[ \cos(78°) \approx 0.2079 \]
Now substituting this value back into the equation for \(d\):
\[ d = \frac{950}{0.2079} \approx 4562.35 \text{ m} \]
Thus, the distance the plane traveled as it was taking off is approximately 4562.35 m.
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