1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Stolb23 [73]
3 years ago
8

Three security cameras were mounted at the corners of a triangles parking lot. Camera 1 was 110 ft from camera 2, which was 137

ft from camera 3. Cameras 1 and 3 were 158 ft apart. Which camera had to cover the greatest angle

Mathematics
1 answer:
Nata [24]3 years ago
6 0

Answer:

<em>Camera 2nd has to cover the maximum angle, i.e. </em>78.70^\circ.

Step-by-step explanation:

Please have a look at the triangular park represented as a triangle \triangle ABC with sides

a = 110 ft

b = 158 ft

c = 137 ft

1st camera is located at point C, 2nd camera at point B and 3rd camera at point A respectively.

We can use law of cosines here, to find out the angles \angle A, \angle B, \angle C

As per Law of cosine:

cos C = \dfrac{a^{2}+b^2-c^2 }{2ab}\\cos B = \dfrac{a^{2}+c^2-b^2 }{2ac}\\cos A = \dfrac{b^{2}+c^2-a^2 }{2bc}

Putting the values of a,b and c to find out angles \angle A, \angle B, \angle C.

cos C = \dfrac{110^{2}+158^2-137^2 }{2\times 110 \times 158}\\\Rightarrow cos C = \dfrac{12100+24964-18769 }{24760}\\\Rightarrow cos C =0.526\\\Rightarrow C = 58.24^\circ

cos B = \dfrac{110^{2}+137^2-158^2 }{2\times 110 \times 137}\\\Rightarrow cos B = \dfrac{12100+18769 -24964}{30140}\\\Rightarrow cos B = \dfrac{5905}{30140}\\\Rightarrow cos B =0.196\\\Rightarrow B = 78.70^\circ

cos A = \dfrac{158^{2}+137^2-110^2 }{2\times 158 \times 137}\\\Rightarrow cos A = \dfrac{24964+18769-12100}{43292}\\\Rightarrow cos A = \dfrac{31633}{43292}\\\Rightarrow cos A = 0.731\\\Rightarrow A = 43.05^\circ

<em>Camera 2nd has to cover the maximum angle</em>, i.e. 78.70^\circ.

You might be interested in
which of the following is the probability that a blue marble will be selected from a bag containing 9 red marbles,6 blue marbles
adell [148]

Answer:

2/11

Step-by-step explanation:

Total number of marbles: 9 + 6 + 7 + 11 = 33

Number of blue marbles: 6

p(blue marble) = 6/33 = 2/11

6 0
3 years ago
Read 2 more answers
What is Qanon a lot of people at school keep talking about it but i dont know what it is
marta [7]
It’s a wide-ranging, completely unfounded theory that says that president trump is waging a secret war against elite satan-worshipping in paeophiles in government, business and the media.
6 0
3 years ago
one angle of a triangle is 2 / 3 of a right angle . the greater of the other to exceed the lesser by 20 degree. Find the angles
jarptica [38.1K]
2/3 of a right triangle is 60 degrees.  Then x + (x+20) + 60 = 180 total.

2x + 80 = 180, so 2x = 100 and x = 50.  The angles are 50, 70 and 60 (degrees)

What do you mean by "grades?"
4 0
3 years ago
When I add two to my number and then multiply it by five, I get thirty. What is my number?
rjkz [21]
30/5= 6
6 - 2 = 4
Your number is four
6 0
3 years ago
Read 2 more answers
point "b" has coordinates of -2,-5 after a translation 4 units down a reflection across the y axisand a translation 6 units up w
monitta
Point b would be at 2,-3
5 0
3 years ago
Other questions:
  • A number n is less than 6 units from 0. Write an absolute value inequality
    13·2 answers
  • Henry's brother is bigger and now his crib must be lowered. Once it's lowered, the m &lt;2 is 30°. What are the rest of the angl
    8·1 answer
  • I don’t know how to do this.
    15·1 answer
  • Graph the linear equation and answer each of the following questions. y=-2x-3
    7·1 answer
  • Mrs. Bennett has a rug that is an equalateral triangle with a perimeter of 12feet. Which could be the length of the sides of the
    11·2 answers
  • a recycling company had 460 pounds of material to sort.to make it easier they split them into boxes with each full box having 14
    10·1 answer
  • Given $f(x) = \frac{\sqrt{2x-6}}{x-3}$, what is the smallest possible integer value for $x$ such that $f(x)$ has a real number v
    11·1 answer
  • Determining Proportionality
    13·2 answers
  • Solve for x. Please look at the picture and answer it. Thank you.
    13·1 answer
  • Given a series discount of 25/25 what is the net cost equivalent?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!