Question
A plane takes off at an angle of 78° and covers a horizontal distance of 950 m. Find the distance the plane traveled as it was taking off.(1 point) Responses 197.52 m 197.52 m 4,569.25 m 4,569.25 m 971.22 m 971.22 m 929.24 m
Answers
GPT-4o mini
To find the distance the plane traveled during its takeoff, we can use the relationship between the horizontal distance, the angle of takeoff, and the actual distance traveled (hypotenuse) using trigonometric functions.
Given:
- Horizontal distance (\(d_x\)) = 950 m
- Angle of takeoff (\(\theta\)) = 78°
We can relate the horizontal distance to the actual distance (hypotenuse) using the cosine function:
\[
\cos(\theta) = \frac{d_x}{d}
\]
Where:
- \(d\) is the distance traveled (the hypotenuse).
- Rearranging gives us:
\[
d = \frac{d_x}{\cos(\theta)}
\]
Calculating this with \(\theta = 78^\circ\):
\[
d = \frac{950 \, \text{m}}{\cos(78^\circ)}
\]
Calculating \(\cos(78^\circ)\):
\[
\cos(78^\circ) \approx 0.2079
\]
Now plug this value into the equation:
\[
d \approx \frac{950 \, \text{m}}{0.2079} \approx 4569.25 \, \text{m}
\]
Thus, the distance the plane traveled as it was taking off is approximately **4,569.25 m**.
Given:
- Horizontal distance (\(d_x\)) = 950 m
- Angle of takeoff (\(\theta\)) = 78°
We can relate the horizontal distance to the actual distance (hypotenuse) using the cosine function:
\[
\cos(\theta) = \frac{d_x}{d}
\]
Where:
- \(d\) is the distance traveled (the hypotenuse).
- Rearranging gives us:
\[
d = \frac{d_x}{\cos(\theta)}
\]
Calculating this with \(\theta = 78^\circ\):
\[
d = \frac{950 \, \text{m}}{\cos(78^\circ)}
\]
Calculating \(\cos(78^\circ)\):
\[
\cos(78^\circ) \approx 0.2079
\]
Now plug this value into the equation:
\[
d \approx \frac{950 \, \text{m}}{0.2079} \approx 4569.25 \, \text{m}
\]
Thus, the distance the plane traveled as it was taking off is approximately **4,569.25 m**.