Question

Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 137 ft from camera 2, which was 153 ft from camera 3. Cameras 1 and 3 were 116 ft apart. Which camera had to cover the greatest angle?
1) camera 2
2) camera 3
3) camera 1
4) cannot tell

Answer 1

Hey...Mark as Brainliast.....Please....

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:

121=sqrt%28140%5E2%2B158%5E2-2%28140%29%28158%29cos%28A%29%29

A=47.44 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.

Answer:

$\blue{\underline{\huge{\bold{\boxed{ANSWER}}}}}$

Step-by-step explanation:

Hey...Mark as Brainliast.....Please....

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:

121=sqrt%28140%5E2%2B158%5E2-2%28140%29%28158%29cos%28A%29%29

A=47.44 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:

121%2Fsin%2847.44%29=140%2Fsin%28B%29

B=58.45 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