Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 151 ft from camera 2, which was 122 ft from camera 3. Cameras 1 and 3 were 139 ft apart. Which camera had to cover the greatest angle?
camera 1
camera 2
cannot tell
camera 3
THANK YOU ^_^!!!!!
its camera 3. ur welcome. :) im in connections too.
Well, let's see if we can figure this out! If we draw a triangle using the given distances, we can determine the lengths of each side. From the information provided, we know that camera 1 is 151 ft from camera 2, camera 2 is 122 ft from camera 3, and camera 1 is 139 ft from camera 3. Now, I won't bore you with a math lesson, but using the laws of cosine, we can calculate the angles.
Alright, let's get to the results. After doing some calculations, it turns out that the angle between camera 1 and camera 2 is around 28.9 degrees, the angle between camera 2 and camera 3 is about 53.7 degrees, and the angle between camera 1 and camera 3 is about 97.4 degrees.
So, based on these results, it seems that camera 3 has to cover the largest angle, which is about 97.4 degrees.
But hey, don't go telling the other cameras about this! We wouldn't want to start a camera rivalry or anything. Safety first, after all!
To determine which camera had to cover the greatest angle, we can use the concept of the Law of Cosines. The law states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
Let's label the sides of the triangle:
Side a = 151 ft (distance between camera 1 and camera 2)
Side b = 122 ft (distance between camera 2 and camera 3)
Side c = 139 ft (distance between camera 1 and camera 3)
Now, let's calculate the angles:
Angle A is opposite side a.
Angle B is opposite side b.
Angle C is opposite side c.
We can calculate angle A using the Law of Cosines:
cos(A) = (b^2 + c^2 - a^2) / (2 * b * c)
cos(A) = (122^2 + 139^2 - 151^2) / (2 * 122 * 139)
cos(A) = (14884 + 19321 - 22801) / (33436)
cos(A) = 11404 / 33436
cos(A) ≈ 0.341
Using the inverse cosine function, we can find angle A:
A ≈ cos^(-1)(0.341)
A ≈ 69.91 degrees
Similarly, we can calculate angle B:
cos(B) = (c^2 + a^2 - b^2) / (2 * c * a)
cos(B) = (139^2 + 151^2 - 122^2) / (2 * 139 * 151)
cos(B) = (19321 + 22801 - 14884) / (41789)
cos(B) = 27238 / 41789
cos(B) ≈ 0.651
B ≈ cos^(-1)(0.651)
B ≈ 49.17 degrees
Finally, we find angle C:
C = 180 - A - B
C = 180 - 69.91 - 49.17
C ≈ 61.92 degrees
Now, we know the angles for each camera:
Camera 1 covers angle A ≈ 69.91 degrees.
Camera 2 covers angle B ≈ 49.17 degrees.
Camera 3 covers angle C ≈ 61.92 degrees.
Therefore, the camera that has to cover the greatest angle is Camera 1.
To determine which camera had to cover the greatest angle, we need to find the distances between all three cameras and use trigonometry to calculate the angles.
Let's label the cameras as follows:
- Camera 1: C1
- Camera 2: C2
- Camera 3: C3
Given information:
- Distance between C1 and C2: 151 ft
- Distance between C2 and C3: 122 ft
- Distance between C1 and C3: 139 ft
To find the angles, we can use the Law of Cosines. Let's find the angles at each camera:
Angle at C1:
Using the Law of Cosines, we have:
cos(angle at C1) = (distance between C1 and C2)^2 + (distance between C1 and C3)^2 - (distance between C2 and C3)^2 / (2 * (distance between C1 and C2) * (distance between C1 and C3))
Substituting the given values, we get:
cos(angle at C1) = (151^2 + 139^2 - 122^2) / (2 * 151 * 139)
cos(angle at C1) = 0.628
Taking the inverse cosine (cos^-1) of this value, we find:
angle at C1 = 50.48 degrees
Similarly, we can find the angles at C2 and C3 using the same procedure:
Angle at C2:
cos(angle at C2) = (distance between C2 and C3)^2 + (distance between C1 and C2)^2 - (distance between C1 and C3)^2 / (2 * (distance between C2 and C3) * (distance between C1 and C2))
angle at C2 = 52.82 degrees
Angle at C3:
cos(angle at C3) = (distance between C1 and C3)^2 + (distance between C2 and C3)^2 - (distance between C1 and C2)^2 / (2 * (distance between C1 and C3) * (distance between C2 and C3))
angle at C3 = 76.69 degrees
Now, to determine which camera had to cover the greatest angle, we compare the three angles:
angle at C1 = 50.48 degrees
angle at C2 = 52.82 degrees
angle at C3 = 76.69 degrees
Therefore, Camera 3 had to cover the greatest angle, which measures 76.69 degrees.
look at my answer to the question below this one.
(Flower - Lily ? , - same type of question, why are you switching names ?)