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 show how 987 is the answer
To find the distance the plane still needs to fly to reach the ground, we can use the tangent function.
Let x be the distance the plane still needs to fly.
From the given information, we can form a right triangle with the height of the triangle being the current altitude of the plane (1,000 feet) and the angle of depression being 12 degrees.
The tangent of an angle is defined as the ratio of the opposite side (height) to the adjacent side (distance).
Therefore, we have:
Tangent(12 degrees) = height / x
tan(12°) = 1,000 / x
To find x, we can rearrange the equation:
x = 1,000 / tan(12°)
Using a calculator, we find that tan(12°) ≈ 0.212556561.
Therefore,
x ≈ 1,000 / 0.212556561 ≈ 4,703.7 feet
Rounding to the nearest foot, the distance the plane still needs to fly to reach the ground is approximately 4,704 feet.