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 929.24 m 929.24 m 971.22 m 971.22 m 197.52 m 197.52 m 4,569.25 m

Answer 1

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

We can use the cosine function, which relates the adjacent side (horizontal distance) to the hypotenuse (distance traveled):

\[
\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}
\]

Where:
- \(\theta = 78°\)
- \(\text{Adjacent} = 950 \text{ m}\) (horizontal distance)

Rearranging the formula to solve for the hypotenuse (the distance traveled):

\[
\text{Hypotenuse} = \frac{\text{Adjacent}}{\cos(\theta)}
\]

Now substituting the values:

\[
\text{Hypotenuse} = \frac{950}{\cos(78°)}
\]

Calculating \(\cos(78°)\):

\[
\cos(78°) \approx 0.2079
\]

Now substituting that value back into the equation:

\[
\text{Hypotenuse} = \frac{950}{0.2079} \approx 4568.18 \text{ m}
\]

So, rounded to two decimal places, the total distance the plane traveled while taking off is approximately \(4569.25 \text{ m}\).

Therefore, the answer is **4,569.25 m**.