Question

a plane is taking off at an angle θ=12 degrees from a horizontal runway. to the nearest foot, find the distance the plane has flown when its altitude is 300 feet from the ground.

Answer 1

We can use trigonometry to solve this problem. Let's define the following variables:

h = altitude of the plane (300 feet)
d = distance flown by the plane (what we want to find)
θ = angle of elevation (12 degrees)

We know that the tangent of an angle is equal to the opposite side (h) divided by the adjacent side (d). So we have:

tan(θ) = h / d

Plugging in the values we know:

tan(12 degrees) = 300 feet / d

We can now solve for d. Take the inverse tangent of both sides to isolate d:

d = 300 feet / tan(12 degrees)

Using a calculator, we find that tan(12 degrees) is approximately 0.2126. Therefore:

d = 300 feet / 0.2126

d ≈ 1412 feet

So, the distance the plane has flown when its altitude is 300 feet from the ground is approximately 1412 feet.