A plane is taking off at an angle 0=12 degrees from a horizontal runaway. To the nearest foot find the t distance the plane has flown when its altitude is 300 feet from the ground.
We can use the trigonometric function tangent to solve this problem.
The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the opposite side is the altitude of the plane (300 feet) and the adjacent side is the distance traveled by the plane (t feet).
Therefore, we have the equation:
tan(12°) = 300 / t
To find t, we can rearrange the equation and solve for t:
t = 300 / tan(12°)
Using a calculator, we find that tan(12°) ≈ 0.211, so
t ≈ 300 / 0.211 ≈ 1421.32
The plane has flown approximately 1421.32 feet when its altitude is 300 feet from the ground. To the nearest foot, the plane has flown 1421 feet.