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)Responses929.24 m929.24 m971.22 m971.22 m197.52 m197.52 m4,569.25 m
Answers
GPT-4o mini
To find the distance the plane traveled during takeoff, we can use trigonometry. We know the horizontal distance (\(d_{\text{horizontal}}\)) and the angle of ascent (\(\theta\)). The relationship can be expressed using the cosine function:
\[
\cos(\theta) = \frac{d_{\text{horizontal}}}{d}
\]
Where:
- \(d\) is the actual distance traveled by the plane.
- \(d_{\text{horizontal}} = 950 \, \text{m}\)
- \(\theta = 78°\)
Rearranging to find \(d\):
\[
d = \frac{d_{\text{horizontal}}}{\cos(\theta)}
\]
Substituting the values into the equation:
1. Calculate \(\cos(78°)\):
\[
\cos(78°) \approx 0.2079
\]
2. Now substitute this value into the equation:
\[
d = \frac{950}{\cos(78°)} \approx \frac{950}{0.2079} \approx 4,570.72 \, \text{m}
\]
So the calculated distance does not match any options provided. Let's verify our calculations using exact angles or a calculator, but based on common decimal approximations, this would give you a distance around 4,570 m.
However, **none of the provided options match** that outcome, so please check the angle, or re-evaluate the conditions stated in the question for any missing context or numerical differences.
Assuming we are limited to the closest option based on your list, the only reasonable answer could be rounding differences; hence I recommend confirming values taken, but closest short distance might imply option **4,569.25 m** if matching range constraints provided.
\[
\cos(\theta) = \frac{d_{\text{horizontal}}}{d}
\]
Where:
- \(d\) is the actual distance traveled by the plane.
- \(d_{\text{horizontal}} = 950 \, \text{m}\)
- \(\theta = 78°\)
Rearranging to find \(d\):
\[
d = \frac{d_{\text{horizontal}}}{\cos(\theta)}
\]
Substituting the values into the equation:
1. Calculate \(\cos(78°)\):
\[
\cos(78°) \approx 0.2079
\]
2. Now substitute this value into the equation:
\[
d = \frac{950}{\cos(78°)} \approx \frac{950}{0.2079} \approx 4,570.72 \, \text{m}
\]
So the calculated distance does not match any options provided. Let's verify our calculations using exact angles or a calculator, but based on common decimal approximations, this would give you a distance around 4,570 m.
However, **none of the provided options match** that outcome, so please check the angle, or re-evaluate the conditions stated in the question for any missing context or numerical differences.
Assuming we are limited to the closest option based on your list, the only reasonable answer could be rounding differences; hence I recommend confirming values taken, but closest short distance might imply option **4,569.25 m** if matching range constraints provided.