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 the answer to the nearest foot
feet
To solve this problem, we can use trigonometry. The angle of depression forms a right triangle with the altitude of the plane and the distance the plane still needs to fly to reach the ground.
In this triangle, the angle of depression is 12°, the altitude is 1,000 feet, and we want to find the distance the plane still needs to fly.
We can use the tangent function to find the distance:
tan(12°) = opposite/adjacent
tan(12°) = (distance to fly)/(1,000 feet)
To solve for the distance, we can rearrange the equation:
(distance to fly) = 1,000 feet * tan(12°)
(distance to fly) ≈ 1,000 feet * 0.2126
(distance to fly) ≈ 212.6 feet
So, the plane still needs to fly about 212.6 feet to reach the ground. Rounded to the nearest foot, the answer is 213 feet.