a plane is descending at a 12 degree angle of depression. if the current altitude of the plane is 1,00 feet, find the distance the plane still needs to fly to reach the ground. round the answer to the nearest foot.
To find the distance the plane still needs to fly to reach the ground, we can use trigonometry.
We can use the tangent function to find the length of the side adjacent to the 12-degree angle (which represents the distance the plane still needs to fly to reach the ground), and the side opposite the 12-degree angle (which represents the current altitude of the plane).
Let x represent the distance the plane still needs to fly to reach the ground.
Therefore, we can set up the following equation:
tan(12 degrees) = opposite/adjacent
tan(12 degrees) = 1,000/x
To solve for x, we can isolate it by multiplying both sides by x:
x * tan(12 degrees) = 1,000
x = 1,000 / tan(12 degrees)
Using a calculator, we find that tan(12 degrees) ≈ 0.2126.
Therefore,
x ≈ 1,000 / 0.2126 ≈ 4,708.37
Rounding the answer to the nearest foot, the distance the plane still needs to fly to reach the ground is approximately 4,708 feet.