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.
Let's assume the distance the plane needs to fly is represented by "x" (in feet).
We have an angle of depression of 12 degrees, which means we have a right triangle formed by the altitude of the plane, the distance it still needs to fly, and the distance from the plane's current altitude to the ground.
The side opposite the angle of depression is the altitude of the plane, which is 1,000 feet. The side adjacent to the angle is the distance the plane still needs to fly, which is "x". Therefore, the tangent of the angle is given by:
tan(12°) = altitude / distance
tan(12°) = 1,000 / x
To isolate "x", we can rearrange the equation:
x = 1,000 / tan(12°)
Using a calculator, we can find the tangent of 12 degrees:
tan(12°) ≈ 0.21255656167
Now, we can substitute this value into the equation:
x = 1,000 / 0.21255656167
x ≈ 4705.7552531
Therefore, the plane still needs to fly approximately 4705.7552531 feet to reach the ground. Rounded to the nearest foot, the distance is 4706 feet.