A plane is descending at a 12° angle of depression. If the current altitude of the plane is 1,000 feet, find the distance the plane still needs to fly to reach the ground. Round to the nearest foot.(1 point)
Write the equation to represent the problem.
Let d be the distance the plane still needs to fly to reach the ground.
In a right triangle, the angle of depression is the angle between the horizontal line and the line of sight (or line of sight and the ground).
In this case, the angle of depression is 12° and the side opposite the angle of depression is the altitude of the plane (1,000 feet).
Using trigonometry, we can write the equation: tan(12°) = 1,000 / d.
Since we want to find d, we can rearrange the equation to solve for d:
d = 1,000 / tan(12°)
Use the equation indicated above to solve for the desired side. Round answer to the nearest tenth.
Using the equation d = 1,000 / tan(12°), we can calculate the value of d as follows:
d = 1,000 / tan(12°)
d ≈ 1,000 / 0.2126
d ≈ 4704.23
Therefore, the plane still needs to fly approximately 4704.23 feet to reach the ground, rounded to the nearest tenth.