A television camera is located along the 40 yard line at a football game. If the camera 20 yards back at the sideline through what angle should it be able to pan in order to cover the entire field of play including end zones which are 10 yards deep

Draw a diagram. The camera must pan to one side through an angle x, and to the other side, through an angle y, where

tan(x) = 50/20
tan(y) = 70/20

Now just add up x and y.

What coprdinates will i use?

who said anything about coordinates? If you draw the diagram using the given values, you will have two right triangles. Their common leg will be the 20 yards from the sideline to the camera. The length of the field (plus the two end zones) will be 120 yards, divided 50:70.

To determine the angle through which the camera should be able to pan, we need to consider the dimensions of the field of play and the camera's location.

Let's break down the problem:

1. The camera is located 20 yards back from the sideline along the 40-yard line.
2. The field of play, including the end zones, is 100 yards long (from one end zone to the other).
3. The end zones are each 10 yards deep.

To calculate the angle, we can use basic trigonometry. The camera's position creates a right triangle with the width of the field of play as the base and the camera-to-sideline distance as the height.

Using the Pythagorean theorem, we can find the length of the field from the camera's position to the opposite end zone:

field length = sqrt(100^2 + 20^2) ≈ 102.2 yards

Now, we can calculate the angle through which the camera should be able to pan to cover the entire field using inverse trigonometry (arctan):

angle = arctan(field length / camera-to-sideline distance)
= arctan(102.2 / 20)
≈ 77.2 degrees

Therefore, the camera should be able to pan through an angle of approximately 77.2 degrees to cover the entire field of play, including the end zones.