Imagine you are at home watching television. you are sitting 6 feet away from your tv which is hung on the wall and the top of it is 8 feet off the ground. which of the following functions correctly represents the angle θ that you make with the top of your television?

Option A

Step-by-step explanation:

We can model the situation by means of a right triangle.

Where the  angle is the angle that you make with the top of the TV.

Then the horizontal distance of 6 feet is the adjacent side and the vertical distance of 8 feet is the opposite side to the angle the.

By definition of the function we know that:

Therefore:

53.1

Step-by-step explanation:

You can trace a right triangle with these features:

- the 6 feet distance represents the horizontal distance from you to the TV, this is the base of the triangle or the adjacent leg

- the 8 feet distance is the vertical distance from the base of the triangle to the TV, this is the height of the triangle or opposite leg.

- the angle theta that you make with the top of your TV is

 tan (theta) = opposite leg / adjacent leg = 8/6 =4/3

=> theta = arctan (4/3) = 53.13 degrees.

53.103 degrees

You can trace a right triangle with these features:

- the 6 feet distance represents the horizontal distance from you to the TV, this is the base of the triangle or the adjacent leg

- the 8 feet distance is the vertical distance from the base of the triangle to the TV, this is the height of the triangle or opposite leg.

- the angle theta that you make with the top of your TV is

 tan (theta) = opposite leg / adjacent leg = 8/6 =4/3

=> theta = arctan (4/3) = 53.13 degrees.

53.103 degrees