To find the distance the plane has flown when its altitude is 300 feet, we can use some basic trigonometry, specifically the sine function, which relates the angle of elevation to the opposite side (altitude) and the hypotenuse (the distance flown).
Given:
- The altitude (opposite side) = 300 feet
- The angle of elevation (θ) = 12°
Using the sine function:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
We can rearrange this to find the hypotenuse (the distance flown):
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting in the values we have:
\[ \text{hypotenuse} = \frac{300}{\sin(12°)} \]
Calculating \(\sin(12°)\):
\(\sin(12°) \approx 0.2079\)
Now substituting this value back into the equation:
\[ \text{hypotenuse} = \frac{300}{0.2079} \approx 1442.31 \text{ feet} \]
Finally, rounding to the nearest foot:
The distance the plane has flown when its altitude is 300 feet is approximately 1442 feet.