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? Check all that applies.
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? Check all that applies.
Solution
The trigonometric function that can be used to determine the horizontal distance the plane must fly to be directly above the building is the tangent function.
Here's why:
The problem describes a right triangle where the altitude of the plane is the opposite side, the horizontal distance the plane must fly is the adjacent side, and the angle of depression is the angle we are concerned with.
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, in this case, we can use the tangent function to find the horizontal distance (adjacent side) using the formula:
tan(angle) = opposite side / adjacent side
Rearranging the formula to solve for the adjacent side gives:
adjacent side = opposite side / tan(angle)
So, the tangent function can be used to solve this problem.
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