SOLUTION: Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 158 ft from camera 2, which was 121 ft from Camera 3. Cameras 1 and 3 were 140 ft apart
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Question 329109: Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 158 ft from camera 2, which was 121 ft from Camera 3. Cameras 1 and 3 were 140 ft apart. Which camera had to cover the greatest angle?
a. camera 2 b. camera 1 c. cannot tell d. camera 3 Answer by galactus(183) (Show Source):
You can put this solution on YOUR website! We can use the law of cosines to find an angle, then it all begins to fall into place.
We have 3 sides and need to find the angle.
camera 1 is angle A, camera 2 is angle B and camera 3 is angle C.
Law of cosines:
degrees.
Now, we can use the law of sines or cosines to find another angle. The third angle can then be found by subtracting the other two from 180.
Law of sines:
degrees at camera 2.
Therefore, the other angle C = 180-(47.44+58.45)=74.11 degrees at camera 3.
angle C at camera 3 gives the largest sweep of the lot. This makes sense because the side opposite angle C is side c, it is the longest length of 158. The distance between camera 1 and 2.
