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.

Answer 1

To find the distance the plane traveled during takeoff, we can use basic trigonometry. The horizontal distance covered (950 m) represents the adjacent side of a right triangle, where the distance traveled by the plane represents the hypotenuse. The angle of ascent is given as 78°.

Using the cosine function:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Here, \(\theta\) is 78°, the adjacent side is 950 m, and the hypotenuse is the distance we want to find, which we'll denote as \(d\).

Rearranging the cosine formula to solve for the hypotenuse:

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

Substituting the known values:

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

Now, we need to calculate \(\cos(78°)\). Using a calculator:

\[
\cos(78°) \approx 0.2079
\]

Now substituting this value back into the equation for \(d\):

\[
d = \frac{950}{0.2079} \approx 4562.35 \text{ m}
\]

Thus, the distance the plane traveled as it was taking off is approximately **4562.35 m**.