Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!!!!!!!

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

Nata [24]

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. $78.70^\circ$ .

6 0

3 years ago

Can somone pls help me plssssss

jeka57 [31]

Answer:

$2\frac{2}{5}$

Step-by-step explanation:

12 divided by 5= 2.4

OR

2 2/5

Hope this helps! :)

4 0

3 years ago

Read 2 more answers

What is the slope of the line 4x+y=-9

olga55 [171]

Answer:

The slope of this line is -4

Step-by-step explanation:

To find the slope, you need to solve the equation for y.

4x + y = -9

y = -4x - 9

The slope in this form is always the coefficient of x, making it -4.

8 0

3 years ago

A handyman charges $30 for supplies and

Art [367]

Answer:

30 hours

Step-by-step explanation:

30+45x=60+45x

45x=30+45x

x=30

8 0

3 years ago

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Which of the following inequalities matches the graph? graph of an inequality with a dashed line through the points (0, 7) and (

stiks02 [169]

Answer:

2x + y < 7

Step-by-step explanation:

First we find the slope of the line that passes through the given points. The formula for slope is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Using our points, we have

$m=\frac{7-5}{0-1}=\frac{2}{-1}=-2$

The y-intercept will be the point where the data crosses the y-axis. All y-intercepts have an x-coordinate of 0; since we already have the point (0, 7), we have the y-intercept at 7. This makes our equation

y = -2x + 7

The inequalities we're given are written in standard form, Ax+By=C. This means we need x and y on the same side of the equals in our equation.

Since the inequality is graphed below the line, we want our inequality to be

y < -2x+7

To move the x-value to the other side of the equation, we will add 2x to each side:

y+2x < -2x+7+2x

y+2x < 7

2x+y < 7

7 0

3 years ago

Read 2 more answers