Question

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)

Answer 1

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.