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.
To solve this problem, we can use trigonometry.
Let x be the distance the plane has flown along the ground when its altitude is 300 feet.
We can use the tangent of the angle of elevation (θ) to find the relationship between the altitude and the distance along the ground.
The tangent of θ is equal to the opposite side (the altitude, 300 feet) divided by the adjacent side (the distance along the ground, x):
tan(12°) = 300 / x
Now, we can solve for x by multiplying both sides of the equation by x:
x * tan(12°) = 300
Divide both sides of the equation by tan(12°):
x = 300 / tan(12°)
Using a calculator, we find tan(12°) is approximately 0.2139698.
x = 300 / 0.2139698
x ≈ 1402.91
Therefore, the distance the plane has flown when its altitude is 300 feet from the ground is approximately 1403 feet.