law of sines and law of cosines

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]1.\\ \\ \frac{sin148}{25}=\frac{sinx}{12}\\ \\ x=sin^{-1}\frac{12sin148}{12}\\ \\ x=32^o\\ \\ 2.\\ \\ x^2=42^2+16^2-2(42)16cos120\\ \\ x^2=2692\\ \\ x=\sqrt{2692}\\ \\ 3.\\ \\ 19^2=17^2+14^2-2(17)14cosx\\ \\ x=cos^{-1}\frac{124}{476}\\ \\ x=74.9^o\\ \\ 4.\\ \\ \frac{sin22}{15}=\frac{sin(180-48-22}{x}\\ \\ x=\frac{15sin110}{sin22}\\ \\ x\approx 37.63[/tex]

Answer 2

Answer:

4. [tex]\displaystyle 38 ≈ x[/tex]

3. [tex]\displaystyle 75° ≈ m∠X[/tex]

2. [tex]\displaystyle 52 ≈ x[/tex]

1. [tex]\displaystyle 15° ≈ m∠X[/tex]

Step-by-step explanation:

Before we begin, here are the formulas for both laws:

Solving for Angles

[tex]\displaystyle \frac{x^2 + y^2 - z^2}{2xy} = cos∠Z \\ \frac{x^2 - y^2 + z^2}{2xz} = cos∠Y \\ \frac{-x^2 + y^2 + z^2}{2yz} = cos∠X[/tex]

Do not forget to use [tex]\displaystyle cos^{-1}[/tex]in the end or you will throw the result off!

Solving for Edges

[tex]\displaystyle y^2 + x^2 - 2yx\:cos∠Z = z^2 \\ z^2 + x^2 - 2zx\:cos∠Y = y^2\\ z^2 + y^2 - 2zy\:cos∠X = x^2[/tex]

Take the square root of the end result or you will throw it off!

-----------------------------------------------------------------------------------

Solving for Angles

[tex]\displaystyle \frac{sin∠Z}{z} = \frac{sin∠Y}{y} = \frac{sin∠X}{x}[/tex]

Do not forget to use [tex]\displaystyle sin^{-1}[/tex]in the end or you will throw the result off!

Solving for Edges

[tex]\displaystyle \frac{z}{sin∠Z} = \frac{y}{sin∠Y} = \frac{x}{sin∠X}[/tex]

_____________________________________________

4. [tex]\displaystyle \frac{15}{sin\:22} = \frac{x}{sin\:110} \hookrightarrow \frac{15sin\:110}{sin\:22} = x \hookrightarrow 37,627178911... = x \\ \\ 38 ≈ x[/tex]

3. [tex]\displaystyle \frac{-19^2 + 17^2 + 14^2}{2[17][14]} = cos∠X \hookrightarrow \frac{-361 + 289 + 196}{476} = cos∠X \hookrightarrow 0,2605042016... = cos∠X; 74,900018217...° = cos^{-1}\:0,2605042016... \\ \\ 75° ≈ m∠X[/tex]

2. [tex]\displaystyle 16^2 + 42^2 - 2[42][16]\:cos\:120 = x^2 \hookrightarrow 256 + 1764 - 1344\:cos\:120 = x^2 \hookrightarrow \sqrt{2692} = \sqrt{x^2}; 2\sqrt{673}\:[or\:51,884487084...] = x \\ \\ 52 ≈ x[/tex]

You could have also used the Law of Sines sinse the base angles are congruent [30°].

1. [tex]\displaystyle \frac{sin\:148}{25} = \frac{sin∠X}{12} \hookrightarrow \frac{12sin\:148}{25} = sin∠X \hookrightarrow 0,2543612468... = sin∠X; 14,735739332...° = sin^{-1}\:0,2543612468... \\ \\ 15° ≈ m∠X[/tex]

I am joyous to assist you at any time.

Related Questions

Answer the photo below thanks

Answers

Answer:

x=50

Step-by-step explanation:

65+65=130

180-130=50

Answer:

50 is the answer

Step-by-step explanation:

this is a isosceles triangle having 65 and 65

then 65 + 65 + x = 180 property of traingle

130 + x = 180

x = 180- 130 = 50

Find and reduce -4/7 x 2/3

What is the answer to this?

Answers

Answer:

-8/21

Step-by-step explanation:

The answer to your asked question is -8/21

Which of the following ordered pairs is not in the solution set of y < 2x − 5

Answers

Answer:

(4,3)

Step-by-step explanation:

Solve the equation:

3<2(4)-5

3<8-5

❌3<3 ❌

3 is not less than three, hence this is the phony

i hope this helps!

Julie earns $9 each week as an allowance. If she spends $5 each week for lunch money and saves the rest, which expression shows how much money she will save in x weeks?

Answers

Answer:

(x)4

Step-by-step explanation:

(x) is the amount of weeks and 4 is the amount of money that is saved every week.

Parallel or perpendicular

Answers

neither, because i’m pretty sure parallel lines have to have the same slope & perpendicular lines have slopes that are opposite reciprocals.... & those lines have neither

what’s the slope_____

Answers

Answer:

-4

Step-by-step explanation:

The formula for finding the slope of a line is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] when the given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. We can take any two points given to us from the table and plug them into that expression. For example, we can use the points (0,0) and (2,-8).

[tex]\frac{y_2-y_1}{x_2-x_1}\\= \frac{-8-0}{2-0}\\= \frac{-8}{2}[/tex]

Simplify the fraction

[tex]= -4[/tex]

Therefore, the slope of the line is equal to -4.

I hope this helps!

I really need help
-21a+35

Answers

Answer:

-7 (3a - 5)

Step-by-step explanation:

Answer:

[tex] - 7(3a - 5)[/tex]

Step-by-step explanation:

you just have to factor out the common term 7.

Please help with 3 thank you!

Answers

Answer:

Step-by-step explanation:

What is the y-intercept?

Answers

I need help with this question!

Answers

Answer:

sorry but don't know this answer

Select the correct answer. One factor of the polynomial 213 3r2 – 3x + 2 is (t – 2), which expression represents the other factor, or factors, of the polynomial? A. (21 + 1) (1 - 1) B. (2r2 + 1) OC. (212 - I + 1) OD. (2x - 1)(1 + 1)

Answers

Answer:

(x - 2)(x + 1)(2x -1)

Step-by-step explanation:

We use synthetic division as a tool for factoring the given expression. The coefficients of the terms given are {2, -3, -3, 2}. If x - 2 is a factor of this expression, then 2 is a root. We perform synthetic division as follows:

2 / 2 -3 -3 2

4 2 -2

-------------------------------

2 1 -1 0

Next, we determine whether or not (2x - 1)(x + 1) represents the remaining factor(s). Using -1 as divisor, we get:

-1 / 2 1 -1

-2 1

---------------------

2 -1 0

Since the remainder is zero, x + 1 must be a factor and (2x - 1) the third factor. Answer D is correct.

The solution is, (x - 2)(x + 1)(2x -1), is the expression represents the other factor, or factors, of the polynomial.

What are Polynomials?

Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.

here, we have,

We use synthetic division as a tool for factoring the given expression. The coefficients of the terms given are {2, -3, -3, 2}. If x - 2 is a factor of this expression, then 2 is a root. We perform synthetic division as follows:

2 / 2 -3 -3 2

4 2 -2

-------------------------------

2 1 -1 0

Next, we determine whether or not (2x - 1)(x + 1) represents the remaining factor(s). Using -1 as divisor, we get:

-1 / 2 1 -1

-2 1

---------------------

2 -1 0

Since the remainder is zero, x + 1 must be a factor and (2x - 1) the third factor. Answer D is correct.

Hence, The solution is, (x - 2)(x + 1)(2x -1), is the expression represents the other factor, or factors, of the polynomial.

Know more about Polynomials here:

brainly.com/question/2833285

#SPJ7

A man shares a $1,200,00 inheritance between his 3 sons in ratio 1: 3: 6. Calculate the difference between the largest share and the smallest share

Answers

Answer:

192+7.68=199.68.

Answer:

Step-by-step explanation:

A and D

I need help with the picture. please

Answers

you have to use the order of operations (PEMDAS)

x=3

7+5(3)

MULTIPLACTION FIRST

7+15= 22

so the first was wrong because she added before multiplying

x= 4/5

7+5(4/5)

MULTIPLICATION FIRST

7+4= 11

the second was wrong because she added before multiplying again

PLS NEED DONE ASAP 10 MINUTES TILL DUE

Answers

Well if 4 blue circles + 1 red triangle = 2 green squares + 1 red triangle, then 2 blue circles = 1 green square

Then 3 red + 2 blue = 1 green + 2 blue, so 3 red = 1 green

If we know these facts then

3 red = 2 blue = 1 green

So the bottom one is 6 reds = 2 greens, or 1 green + 2 blue.

This makes my head hurt. They’re making it harder than it is.

Hope I didn’t confuse you more.

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. If and , what is ? Write your answer in simplest form. When and , .

Answers

7920+48202849+820-891

A rectangular playground is 65m long and 30 m wide. A pathway of 1.5 m width goes all around, outside it. Find the area of the pathway

Answers

Answer:

97.5 m^2

Step-by-step explanation:

Given data

Length = 65m

Width= 30m

We are told that the width of the path= 1.5m

Hence the area of the path is

=65*1.5

=97.5 m^2

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