A plane is descending at a 19° angle of depression. If the current altitude of the plane is 1,250 feet, find the distance the plane still needs to fly to reach the ground. Round the answer to the nearest foot
Let's call the distance the plane still needs to fly to reach the ground x.
In a right triangle formed by the plane, the ground, and the line of sight, the angle of depression is the angle between the horizontal line and the line of sight.
In this case, the angle of depression is given as 19°.
Since the plane is descending, the altitude decreases, which means the length of the opposite side of the triangle decreases as well.
This opposite side represents the altitude of the plane, which is given as 1,250 feet.
We can use trigonometry to find the length of the adjacent side (the distance the plane still needs to fly).
Since tan(theta) = opposite/adjacent, where theta is the angle of depression, we have:
tan(19°) = 1250 / x
To isolate x, we multiply both sides by x and divide by tan(19°):
x = 1250 / tan(19°)
Using a calculator, tan(19°) is approximately 0.345, so we can substitute it into the equation:
x = 1250 / 0.345
x ≈ 3623.1884057971
Rounded to the nearest foot, the plane still needs to fly about 3623 feet to reach the ground. Answer: \boxed{3623 \text{ feet}}.