Question

A plane takes off at an angle of 78° and covers a horizontal distance of 850 m. Find the distance the plane traveled as it was taking off.





(1 point)
Responses

4088.27 m
4088.27 m

4569.25 m
4569.25 m

868.99 m
868.99 m

176.72 m

Answer 1

To find the distance the plane traveled as it was taking off, we can use the relationship between the horizontal distance traveled, the angle of takeoff, and the total distance traveled (which we'll denote as \(d\)).

The horizontal distance \(x\) traveled can be expressed using the cosine of the angle of takeoff:

\[
x = d \cdot \cos(\theta)
\]

where:
- \(x\) is the horizontal distance (850 m),
- \(d\) is the total distance traveled,
- \(\theta\) is the angle of takeoff (78°).

We need to solve for \(d\):

\[
d = \frac{x}{\cos(\theta)}
\]

Substituting the values, we have:

\[
d = \frac{850}{\cos(78°)}
\]

First, we calculate \(\cos(78°)\):

\[
\cos(78°) \approx 0.2079
\]

Now we can find \(d\):

\[
d = \frac{850}{0.2079} \approx 4090.74 \text{ m}
\]

Looking for a match with the provided options, the closest practical value would be:

**4088.27 m**

Thus, the plane traveled approximately **4088.27 m** as it was taking off.