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. ,
We can use trigonometry to solve this problem. The angle of depression is the angle formed between the line of sight from the plane to the ground and a horizontal line. We can consider this as the angle between the line of sight from the plane to the ground and a vertical line.
Let's assume that the distance the plane still needs to fly to reach the ground is x feet.
In a right triangle, the tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the altitude of the plane (1,250 feet) and the adjacent side is the distance the plane still needs to fly (x feet).
So we have the equation:
tan(19°) = 1,250 / x
To solve for x, we can rewrite this equation as:
x = 1,250 / tan(19°)
Using a calculator, we find that the tangent of 19° is approximately 0.3513.
So x = 1,250 / 0.3513 ≈ 3,557.5436
Rounding to the nearest foot, the plane still needs to fly approximately 3,558 feet to reach the ground.