Imagine that you are sitting 6 feet away from a television that is hung on a wall. The top of the TV is 8 feet off the ground. Which function correctly represents the angle that you make with the top of your television?
The Tangent Function:
tanA = Y/X = 8/6.
To determine the correct function that represents the angle you make with the top of the television, we can use some basic trigonometric principles.
In this scenario, we can draw a right triangle, where the distance between you and the television is the base of the triangle, the height of the television is the opposite side, and the angle you make with the top of the television is the angle θ (theta).
Since the top of the television is 8 feet off the ground, and you are sitting 6 feet away from the television, we can label the triangle as follows:
Base (adjacent side) = 6 feet
Height (opposite side) = 8 feet
Angle θ (theta) = the angle you make with the top of the television
Now, we need to determine which trigonometric function relates the given sides of the right triangle. There are three primary trigonometric functions: sine (sin), cosine (cos), and tangent (tan).
Sin θ = Opposite/Hypotenuse
Cos θ = Adjacent/Hypotenuse
Tan θ = Opposite/Adjacent
Since we know the base and height of the triangle, we can use the tangent function because it relates the opposite side (height) to the adjacent side (base). Hence, the correct function to represent the angle θ is:
Tan θ = Opposite/Adjacent
Tan θ = 8/6
Tan θ = 4/3
Therefore, the correct function that represents the angle you make with the top of your television is:
tan θ = 4/3