To find the distance \( x \) from the plane (P) to the observer (O), we can use the relationship in a right triangle involving the angle of elevation and the altitude.
The altitude of the plane is the opposite side of the triangle, while \( x \) is the hypotenuse.
From trigonometry, we can use the sine function to find the hypotenuse:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
where \( \theta \) is the angle of elevation (35°) and the opposite side is the altitude (17,000 feet).
Rearranging the formula to solve for the hypotenuse \( x \):
\[ \sin(35°) = \frac{17,000}{x} \]
\[ x \cdot \sin(35°) = 17,000 \]
\[ x = \frac{17,000}{\sin(35°)} \]
Now we can calculate \( x \):
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Find \( \sin(35°) \): \[ \sin(35°) \approx 0.5736 \]
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Substitute into the equation: \[ x = \frac{17,000}{0.5736} \approx 29,635 \text{ feet} \]
Rounding this, we find:
\[ x \approx 29,639 \text{ feet} \]
Thus, the distance from the plane to the observer is approximately 29,639 feet.