To find \( x \), which presumably refers to the horizontal distance from the point on the runway directly beneath the plane to the point where the plane takes off, we can use trigonometry.
The plane is at a height (altitude) of 250 ft and is taking off at an angle of 15 degrees. We will use the tangent function, which relates the angle to the opposite side (altitude) and the adjacent side (horizontal distance).
The tangent of an angle in a right triangle is given by the formula:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case, \( \theta = 15^\circ \) and the opposite side (altitude) is 250 ft, while the adjacent side is what we are trying to find (\( x \)). Therefore, we can write:
\[ \tan(15^\circ) = \frac{250}{x} \]
To find \( x \):
- Rearrange the equation to solve for \( x \):
\[ x = \frac{250}{\tan(15^\circ)} \]
- Calculate \( \tan(15^\circ) \). The approximate value is:
\[ \tan(15^\circ) \approx 0.2679 \]
- Plug the value back into the equation:
\[ x \approx \frac{250}{0.2679} \approx 933.03 \]
- Rounding this to the nearest whole number, we get:
\[ x \approx 933 \]
Thus, the horizontal distance \( x \) is approximately 933 feet.