A plane is taking off at an angle θ=12° from a horizontal runway. To the nearest foot, find the distance the plane has flown when its altitude is 300 feet from the ground. (1 point)
We can use trigonometry to solve this problem.
Let the distance the plane has flown be represented by x feet.
We can set up a right triangle with the altitude (300 feet) as the opposite side and the distance flown (x feet) as the adjacent side. The angle θ (12°) is the angle between the runway and the hypotenuse of the triangle.
We can use the tangent function to find x:
tan(12°) = opposite/adjacent
tan(12°) = 300/x
To isolate x, we can cross-multiply and solve for x:
x * tan(12°) = 300
x = 300/tan(12°)
Using a calculator, we find that tan(12°) ≈ 0.2125566.
Therefore,
x = 300/0.2125566
x ≈ 1412.0513
Rounding to the nearest foot, the distance the plane has flown when its altitude is 300 feet from the ground is approximately 1412 feet.