You are watching the sky and notice that a plane is taking off at an angle
θ=11°
from a horizontal runway. Part 1:To the nearest foot, find the distance the plane has flown when its altitude is 550 feet from the ground. Part 2: To the nearest foot, find the distance the you are from the airport horizontal runway if you were standing on the ground at the right angle?
Part 1:
To find the distance the plane has flown when its altitude is 550 feet from the ground, we can use trigonometry. The vertical component of the plane's motion can be represented by the equation:
altitude = distance * sin(θ)
Rearranging the equation, we have:
distance = altitude / sin(θ)
Plugging in the values: altitude = 550 feet and θ = 11°,
distance = 550 / sin(11°) ≈ 3056 feet
Therefore, to the nearest foot, the distance the plane has flown when its altitude is 550 feet from the ground is approximately 3056 feet.
Part 2:
To find the distance you are from the airport's horizontal runway if you were standing on the ground at a right angle, we can again use trigonometry.
The horizontal distance can be represented by the equation:
distance = altitude * tan(θ)
Plugging in the values: altitude = 550 feet and θ = 11°,
distance = 550 * tan(11°) ≈ 110.04 feet
Therefore, to the nearest foot, the distance you are from the airport horizontal runway is approximately 110 feet.