Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 106 ft from camera 2, which was 133
ft from camera 3. Cameras 1 and 3 were 151 ft apart. Which camera had to cover the greatest angle?]
A. Camera 3
B. Cannot tell
C. Camera 2
D. Camera 1
A. Camera 3
B. Cannot tell
C. Camera 2
D. Camera 1
1 answer:
Correct Answer:
Option C. Camera 2
The greatest angle is always opposite to the side measure greater in length. So first we find the greatest side.
The distance between cameras is:
Camera 1 and Camera 2 : 106 feet
Camera 2 and Camera 3 : 133 feet
Camera 1 and Camera 3 : 151 feet
So the largest side of the triangle is the side between camera 1 and camera 3. So the camera opposite to this side will have to cover to greatest angle. The camera opposite to this side is Camera 2. This scenario is also shown in figure below.
Therefore, Camera 2 had to cover the greatest angle.
Option C. Camera 2
The greatest angle is always opposite to the side measure greater in length. So first we find the greatest side.
The distance between cameras is:
Camera 1 and Camera 2 : 106 feet
Camera 2 and Camera 3 : 133 feet
Camera 1 and Camera 3 : 151 feet
So the largest side of the triangle is the side between camera 1 and camera 3. So the camera opposite to this side will have to cover to greatest angle. The camera opposite to this side is Camera 2. This scenario is also shown in figure below.
Therefore, Camera 2 had to cover the greatest angle.
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Answer:
Answer choice D:
y - 6 = 2(x - 5)
Step-by-step explanation:
This question is basically asking you to find the point-slope form equation for a line going through the points (3, 2) and (5, 6).
As you can tell by the name, point-slope form needs both a point that the line goes through and the slope of the line.
You can find the slope of the line by using the slope formula since you have two points that the line goes through.
Slope formula:
Substitute in the points A and B into the formula.
The slope of this line is 2.
Now since we have the slope and a point of the line, we can plug this into the point-slope form equation, which is y - y1 = m(x - x1).
We will be using one of the points (I will be using point A) to substitute the coordinates into y1 and x1, and using the slope to substitute into m.
Substitute point A's coordinates and the slope of the line into the point-slope form equation.
y - (2) = 2(x - (3))
I always put parentheses around the numbers I substitute into an equation to see exactly what is being plugged in, but now you can remove them to find your answer.
y - 2 = 2(x - 3)
Now, since none of the answer choices do not fit with the answer we have found, we can use the other point coordinate-- point B.
Substitute point B and the slope 2 into the equation.
y - (6) = 2(x - (5))
Remove the parentheses.
y - 6 = 2(x - 5)
There is an answer choice for this answer we have found, answer choice D.
By the way, both of the equations we found: y - 2 = 2(x - 3) and y - 6 = 2(x - 5) will yield the same answer in the end so don't worry if one of the points don't work if you have a multiple choice like this question.