An airplane flies at an altitude of 3.2 km. The angle of depression from the plane to the base of a building is 52 degrees . What trigonometric function (s) will be able to determine the horizontal distance must the plane fly to be directly above the building?
Question
An airplane flies at an altitude of 3.2 km. The angle of depression from the plane to the base of a building is 52 degrees . What trigonometric function (s) will be able to determine the horizontal distance must the plane fly to be directly above the building?
Solution
To solve this problem, we can use the concept of trigonometric functions. In this case, we are dealing with a right triangle where the altitude of the plane is the opposite side and the horizontal distance the plane must fly is the adjacent side. The angle of depression given is the angle between the horizontal line from the plane and the line to the base of the building.
The trigonometric function that relates the adjacent side (which is what we're trying to find) and the opposite side (which we know) is the tangent function.
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. So, we can set up the equation as follows:
tan(52 degrees) = 3.2 km / x km
Where x is the horizontal distance the plane must fly to be directly above the building. By rearranging the equation, we can solve for x:
x km = 3.2 km / tan(52 degrees)
So, the tangent function can be used to determine the horizontal distance the plane must fly to be directly above the building.
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