Question

a plane takes off at an angle of 78 degrees and covers a horizontal distance of 950 m, find the distance the plane traveled as it was taking off

Answer 1

To find the distance the plane traveled during takeoff, we can use the horizontal distance and the angle of takeoff to calculate the hypotenuse of the right triangle formed.

Given:
- Horizontal distance (\(d_{horizontal}\)) = 950 m
- Angle of takeoff (\(\theta\)) = 78 degrees

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

The formula is:
\[
\cos(\theta) = \frac{d_{horizontal}}{d_{hypotenuse}}
\]

Rearranging the formula to find the hypotenuse:
\[
d_{hypotenuse} = \frac{d_{horizontal}}{\cos(\theta)}
\]

Now, plug in the values:
\[
d_{hypotenuse} = \frac{950}{\cos(78^\circ)}
\]

Now, we need to calculate \( \cos(78^\circ) \). Using a calculator:
\[
\cos(78^\circ) \approx 0.2079
\]

Now we can calculate \(d_{hypotenuse}\):
\[
d_{hypotenuse} = \frac{950}{0.2079} \approx 4566.7 \, \text{m}
\]

Therefore, the distance the plane traveled as it was taking off is approximately **4566.7 meters**.