SOLUTION: A television camera is 30 ft from the sideline of a basketball court 94ft long. The camera is located 7ft from midcourt. Through what angle must it sweep in order to cover all acti

Algebra ->  Linear-equations -> SOLUTION: A television camera is 30 ft from the sideline of a basketball court 94ft long. The camera is located 7ft from midcourt. Through what angle must it sweep in order to cover all acti      Log On


   

Question 1121876: A television camera is 30 ft from the sideline of a basketball court 94ft long. The camera is located 7ft from midcourt. Through what angle must it sweep in order to cover all action on the court?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Since you say the camera is 30 feet from the sideline, I assume the "7 feet from midcourt" means it is 40 feet from one end of the court and 54 feet from the other end.

Here is a rough picture (not to scale):



The angle the camera (at C) must sweep to cover all action on the court is angle ACB, which is the sum of angles ACO and BCO. Angle ACO has a tangent of 40/30; angle BCO has a tangent of 54/30; so the measure of angle ACB is

arctan(40/30)+arctan(54/30)

which is about 114 degrees.