SOLUTION: A security camera needs to be set so that it's angle of view includes the area from a doorway to the edge of a parking lot. The doorway is 16m from the camera. The edge of the park

Algebra ->  Trigonometry-basics -> SOLUTION: A security camera needs to be set so that it's angle of view includes the area from a doorway to the edge of a parking lot. The doorway is 16m from the camera. The edge of the park      Log On


   

Question 1037406: A security camera needs to be set so that it's angle of view includes the area from a doorway to the edge of a parking lot. The doorway is 16m from the camera. The edge of the parking lot is 24m from the camera. The doorway is 28m from the edge of the parking lot. What angle of view is needed for the camera?
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Doorway to Camera, 16 meter leg
Parking Lot Edge to Camera, 24 meter hypotenuse
Parking Lot Edge to Doorway, 28 meter leg


This is not a right triangle. Change the names of the sides to this:
Doorway to Camera, 16 meter side
Parking Lot Edge to Camera, 24 meter side
Parking Lot Edge to Doorway, 28 meter side
...
and to be sure,
16%5E2%2B24%5E2%3C%3E28%5E2
256%2B576%3C%3E784
832%3C%3E784

Law Of Cosines will use the unknown angle at the camera. The distance from doorway to edge of the parking lot is the side opposite the camera.
-
16%5E2%2B24%5E2-2%2A16%2A24%2Acos%28c%29=28%5E2

832-2%2A16%2A24%2Acos%28c%29=28%5E2
-2%2A16%2A24%2Acos%28c%29=28%5E2-832
cos%28c%29=%2828%5E2-832%29%2F%28-2%2A16%2A24%29
cos%28c%29=48%2F%282%2A16%2A24%29
cos%28c%29=1%2F%2816%29

Angle measure c is arcos(1/16) or cos%5E-1%281%2F16%29.
86 degrees.