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

197.52 m
197.52 m

4,569.25 m
4,569.25 m

929.24 m
929.24 m

Answer 1

To find the distance the plane traveled during takeoff, we can use trigonometry. The horizontal distance covered is the adjacent side of a right triangle formed by the distance traveled (the hypotenuse) and the angle of elevation (78°).

Let \( d \) be the distance the plane traveled. The horizontal distance covered is given by:

\[
\text{Horizontal Distance} = d \cdot \cos(\theta)
\]

Substituting the given values:

\[
950 = d \cdot \cos(78°)
\]

Now, we can solve for \( d \):

\[
d = \frac{950}{\cos(78°)}
\]

Using \( \cos(78°) \):

\[
\cos(78°) \approx 0.2079
\]

Now substituting this value:

\[
d = \frac{950}{0.2079} \approx 4569.25 \text{ m}
\]

So the distance the plane traveled as it was taking off is approximately **4,569.25 m**.

The correct answer is:

**4,569.25 m**.