Final answer:
The distance from the airport at which the plane is when it starts its descent can be calculated using trigonometry by finding the adjacent side of a right-angled triangle formed by the descent angle of 8° and the altitude of 25,000 ft.
Step-by-step explanation:
The student has asked how far from the airport the plane is, assuming it starts its descent from 25,000 ft at an angle of 8° below the horizontal. To solve this problem, we need to use trigonometry. The horizontal distance the plane needs to travel before it lands can be found by calculating the adjacent side of a right-angled triangle, where the angle of descent is 8° and the opposite side is the altitude of 25,000 ft.
We can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle:
tan(θ) = opposite / adjacent
Rearranging the formula to solve for the adjacent side (horizontal distance), we have:
adjacent = opposite / tan(θ)
By plugging in the values:
- opposite = 25,000 ft
- θ = 8°
We can then calculate the horizontal distance. Note that it is essential to convert the angle into radians if the calculator being used requires it, or to set the calculator to degree mode if it has one.