An airplane flying at an altitude of 5100 ft is 12000 feet from an airport. what is the angle of elevation of the plane?
I don't know how to start the problem.
as usual, draw a diagram, and review your basic trig function definitions:
tan θ = 5100/12000
So,
θ = arctan(51/120)
23
To find the angle of elevation of the plane, you need to use trigonometry. Specifically, you can use the tangent function (tan) to find the angle.
First, let's label the important elements of the problem:
- The altitude of the plane is 5100 ft.
- The distance between the plane and the airport is 12000 ft.
Now, recall that tangent (tan) of an angle can be found by dividing the opposite side by the adjacent side in a right triangle.
In this case, the opposite side is the altitude of the plane (5100 ft), and the adjacent side is the distance between the plane and the airport (12000 ft).
So, you can use the following formula to find the tangent of the angle of elevation:
tan(angle of elevation) = opposite/adjacent
Plugging in the given values:
tan(angle of elevation) = 5100/12000
Now, to find the angle of elevation itself, you need to take the inverse tangent (arctan) of both sides of the equation.
angle of elevation = arctan(5100/12000)
To solve this, you can use a scientific calculator or an online trigonometric calculator to find the inverse tangent of 5100/12000. The result will be the angle of elevation of the plane.