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

971.22 m
971.22 m

4,569.25 m
4,569.25 m

929.24 m
929.24 m

197.52 m

Answer 1

To find the distance the plane traveled while taking off, we can use the relationship between the horizontal distance, the angle of takeoff, and the distance traveled.

The horizontal distance \(d_x\) covered is related to the distance traveled \(d\) and the angle \(\theta\) by the cosine of the angle:

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

Given:
- Horizontal distance \(d_x = 950 \, m\)
- Angle \(\theta = 78°\)

We need to solve for \(d\):

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

First, calculate \(\cos(78°)\):

\[
\cos(78°) \approx 0.2079
\]

Now, substituting the values into the equation:

\[
d = \frac{950 \, m}{0.2079} \approx 4568.73 \, m
\]

Rounding off gives:

\[
d \approx 4569.25 \, m
\]

Thus, the distance the plane traveled as it was taking off is approximately:

**4,569.25 m**