a plane flying 33,000 ft is 130 miles from the airport when it begins to descend if the angle of descent is constant find this angle
33000 ft = 33000/5280 miles = 5.681818... miles
let the angle of descent be Ø
tanØ = 5.681818.../130 = .043706...
Ø = appr 2.5°
To find the angle of descent, we can use basic trigonometry. We have the height of the plane (33,000 ft) and the distance from the airport (130 miles). Let's assume the angle of descent is represented by θ.
We can use the tangent function to find the angle:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the plane and the adjacent side is the distance from the airport. Let's convert the height from feet to miles:
33,000 ft = 33,000/5,280 miles = 6.25 miles (approximately)
Now, we can substitute the values into the equation:
tan(θ) = 6.25 miles / 130 miles
To find the angle, we can take the inverse tangent (arctan) of both sides:
θ = arctan(6.25/130)
Using a calculator, we can find:
θ ≈ 2.77 degrees
Therefore, the angle of descent is approximately 2.77 degrees.
To find the angle of descent, we can use trigonometry.
Let's assume that the angle of descent is represented by θ (theta).
In a right triangle, the opposite side is the change in altitude (33,000 ft) and the adjacent side is the horizontal distance (130 miles) covered during the descent.
Now, to find the angle θ, we need to use the tangent function:
tan(θ) = opposite side / adjacent side
tan(θ) = 33,000 ft / (130 miles * 5280 ft/mile) [converting miles to feet]
tan(θ) = 33,000 ft / (686,400 ft)
tan(θ) ≈ 0.048 = 48/1000
Taking the arctangent (inverse tangent) of both sides, we get:
θ ≈ arctan(0.048)
Using a scientific calculator or an online tool, we find:
θ ≈ 2.75 degrees
Therefore, the angle of descent for the plane is approximately 2.75 degrees.