Answer:
32/13
Step-by-step explanation:
To evaluate the expression Z₂ * Z3 / Z₁, we first need to find the complex numbers Z₂ * Z3 and Z₁.
Z₂ * Z3 = -2 + 3i * 4 + 2i = (-8 + 14i) + (-6 + 6i) = -8 + 8i
Z₁ = 3 - 2i
So, Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i)
We can simplify this expression by multiplying the numerator and denominator by the complex conjugate of the denominator, which is (3 + 2i).
Z₂ * Z3 / Z₁ = (-8 + 8i) / (3 - 2i) * (3 + 2i) / (3 + 2i) = (-8 + 8i) * (3 + 2i) / (3 - 2i) * (3 + 2i)
Z₂ * Z3 / Z₁ = ((-8 * 3 + 8 * 2i) + (8 * 3 + 8 * 2i)) / (3^2 + (-2i)^2) = (16 + 16i) / 13
Therefore, Z₂ * Z3 / Z₁ = (16 + 16i) / 13.
What else must you know to prove the triangles congruent by ASA? By SAS?
The proof of congruence by SAS, then 2 corresponding sides and the corresponding included angles of both triangles are equal.
What are congruent angles?Angles who are of same measurement are called congruent.
Suppose that two angles ∠A and ∠B are of same measure, then
[tex]m\angle A = m\angle B[/tex]is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.
The SAS postulate , Two sides and the included angle of one triangle are identical to the corresponding two sides and the included angle of another triangle.
In the triangle, the angles mCAD and mACB are congruent.
m∠CAD ≅ m∠ACB
Since m∠CAD and m∠ACB are congruent, AD and BC must also be congruent.
As a result, the SAS Congruence postulate is proven.
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Solve the given inequality. Enter your solution in interval notation. Use exact values.
The solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).
What is inequality?
An inequality is a mathematical statement that describes a relationship between two values or expressions, where one is greater than, less than, or not equal to the other.
To solve the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex], we can use the concept of interval notation and test each interval to see if it satisfies the inequality. Here are the steps:
Find the critical points of the expression, which are the values that make the expression equal to zero. In this case, the critical points are -5, -4, and -3.
Use these critical points to divide the number line into four intervals: (-∞, -5), (-5, -4), (-4, -3), and (-3, ∞).
Test a value in each interval to see if the inequality is true or false. We can use the sign of the expression to determine this:
For x < -5, all three factors are negative, so the product is negative. Therefore, this interval does not satisfy the inequality.
For -5 < x < -4, the first factor is positive and the other two factors are negative. The product is therefore negative. This interval does not satisfy the inequality.
For -4 < x < -3, the first and third factors are positive and the second factor is negative. The product is therefore positive. This interval satisfies the inequality.
For x > -3, all three factors are positive, so the product is positive. Therefore, this interval satisfies the inequality.
Write the solution set using interval notation. We have found that the solution set is (-4, -3) union ( -3, ∞).
Therefore, the solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).
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After four years in college, Josie owes $50000 in student loans. The interest rate on the federal loans is 2.8% and the rate on the private bank loans is 4.8%. The total interest she owes for one year was $1,600.00.What is the amount of each loan?
Federal loan at 2.8% account = $
Private bank loan at 4.8% account = $
The federal loan at 2.8% is approximately 11000, and the private bank loan at 4.8 percent is around 39000 (which is 50000 - 11000).
How to solve the problem?Let's use f and p to denote the amounts of Josie's federal and private bank loans, respectively.
We know that the total amount of loans is 50000, so:
f + p = 50000
We also know that the interest on federal loans at 2.8% and the interest on private bank loans at 4.8% add up to 1600 per year. The interest on the federal loans is 0.028f and the interest on the private bank loans is 0.048p, so:
0.028f + 0.048p = 1600
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for p:
p = 50000 - f
Substituting this into the second equation, we get:
[tex]0.028f + 0.048(50000 - f) = 1600[/tex]
Simplifying and solving for [tex]f[/tex], we get:
[tex]f = \frac{1600 - 0.048 \cdot 50000}{0.02} \approx 11000[/tex]
Therefore, the federal loan at 2.8% is approximately 11000, and the private bank loan at 4.8% is approximately 39000 (which is 50000 - 11000).
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Find the unknown side length.
Answer:
x = 2.4 inch
Step-by-step explanation:
Tall retangular prism = lwh = 6 x 9 x 3 = 162 in^3
378 - 162 = 216
Long rectangular prism = lwh = (15)(6)(x) = 90x
216 = 90x
x = 2.4
2. Calculate the surface area and volume of a square pyramid
10cm
12cm
10cm
Answer:
Surface are = 340 cm²; Volume = 363.33 cm³.------------------------------
Full surface area is the sum of areas of 4 triangles and the square base:
S = 4*1/2*10*12 + 10² S = 240 + 100S = 340 cm²Find the height h of the pyramid, using slant height and the side of the base and Pythagorean:
h² = 12² - (10/2)²h² = 144 - 25h² = 119h = √119 ≈ 10.9 cmFind the volume:
V = 1/3*a²hV = 1/3*10²*10.9V = 363.33 cm³Find the common difference of the arithmetic sequence -1,7,15,…
The common difference of the given arithmetic sequence is 8.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.
The given arithmetic sequence is -1, 7, 15,....
Common difference = Second term - First term
= 7-(-1)
= 7+1=8
Common difference = Third term - Second term
= 15-7
= 8
Therefore, the common difference is 8.
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The solution is, the common differences are -3, -20, -10, -2, 5.
What is common difference?In an arithmetic sequence, the difference between any two consecutive terms must always be the same number, which is known as the common difference.
here, we have,
So we just need to take different pairs of consecutive terms and see if their difference is always the same:
1) The differences are:
32 - 35 = -3
29 - 32 = -3
26 - 29 = -3
So yes, this is an arithmetic sequence and the common difference is -3
2) The differences are:
-23 - (-3) = -20
-43 - (-23) = -20
-63 - (-43) = -20
This is an arithmetic sequence, and the common difference is -20
3) The differences are:
-64 -(-34) = -30
-94 -(-64) = -30
-124 -(-94) = -30
This is an arithmetic sequence and the common difference is -30
4) The differences are:
-40 -(-30) = -10
-50 - (-40) = -10
-60 - (-50) = -10
This is an arithmetic sequence and the common difference is -10
5) The differences are:
-9 - (-7) = -2
-11 - (-9) = -2
-13 - (-11) = -2
This is an arithmetic sequence, and the common difference is -2
6) The differences are:
14 - 9 = 5
19 - 14 = 5
24 - 19 = 5
This is an arithmetic sequence, and the common difference is 5.
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Consider the function below.
f(x)=8/x−6
What would be the output if the input is 8?
8/14
8/6
2 1/3
4
The input is 8, the output of the function f(x) would be -5.
What is the function?
Function is a relationship or expression involving one or more variables. It has a set of input and outputs.
Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet
To find the output of the function f(x) when x is 8, we substitute x = 8 into the function and simplify:
f(x) = 8/x - 6
f(8) = 8/8 - 6
f(8) = 1 - 6
f(8) = -5
Hence, if the input is 8, the output of the function f(x) would be -5.
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Please help I have no clue on what to do I will give you guys multiple points if you are able to help.
Based on the information, we can infer that the graph would be a curve like the one shown in the attached image.
How to graph this information?First of all, to graph the information about the body temperature of children, we must consult on the internet or other sources what is the body temperature of children. Below is the information:
The average body temperature is 98.6 F (37 C). But normal body temperature can range between 97 F (36.1 C) and 99 F (37.2 C) or more.According to the above, the graph should present a higher frequency at a temperature of 98.6, so the highest point on the graph would be at that temperature. On the other hand, the other temperatures would decrease because they are less frequent among children.
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Solve the equation
below. Show all of your
work.
20= m÷-5
Answer:
The solution to the equation 20 = m ÷ -5 is m = -100
To see this, we can multiply both sides of the equation by -5 to isolate the variable m:
20 × -5 = m ÷ -5 × -5
Expanding the right side of the equation:
20 × -5 = m × 1
Combining like terms:
-100 = m
And the solution is:
m = -100
Verification:
To verify the solution, we can plug in the value of m back into the original equation and see if it is true:
20 = -100 ÷ -5
Expanding -100 ÷ -5:
20 = 20
Since 20 = 20 is a true statement, we have verified that the solution m = -100 is correct.
Simplify the trigonometric expression below by writing the simplified form in terms of sin(x).
tan(x)+cot(x)/sec(x)=
The expression can be simplified to: [tex]tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]
How to simplifyWe can simplify the expression as follows:
tan(x) + cot(x)/sec(x) = tan(x) + 1/tan(x) / 1/cos(x) = tan(x) + cos(x) / tan(x) * cos(x) = tan(x) + cos^2(x) / tan(x)
Using the identity: tan(x)^2 + 1 = sec^2(x), we can simplify further:
tan(x) + cos^2(x) / tan(x) = tan(x) + cos^2(x) / (sqrt(sec^2(x) - 1)) = tan(x) + cos^2(x) / sqrt(tan^2(x) + 1 - 1) = tan(x) + cos^2(x) / sqrt(tan^2(x))
Using the identity sin^2(x) + cos^2(x) = 1, we can simplify further:
[tex]tan(x) + cos^2(x) / \sqrt(tan^2(x)) = tan(x) + (1 - sin^2(x)) / \sqrt(tan^2(x)) = tan(x) + \sqrt(1 - sin^2(x)) / \sqrt(tan^2(x)) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]
Therefore, the expression can be simplified to:
[tex]tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]
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Paying for First Dates USA Today posted this question on the electronic version of its newspaper: “Should guys pay for the first date?” Of the 1148 subjects who decided to respond, 85% of them said “yes.” What is wrong with this survey? Is the value of 85% a statistic or a parameter? Does the survey constitute an experiment or an observational study?
On solving the provided question we cans ay that the statistical data In this instance, the subject is not treated by the researcher.
what are statistical data?Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts A data element is a feature (or attribute) data such as height, origin country, income, etc. that is measured or tallied. Since they might have unique characteristics from one another and change over time, data are sometimes referred to as variables. Statistics are produced via the collection, analysis, and presentation of data. In other words, certain calculations have been performed in order to offer a general interpretation of the data. Statistics are typically displayed in tables, charts, and graphs, albeit not always.
Due to the fact that these replies are not random, they may not accurately represent the population.
because they chose themselves.
The majority of the sample proportion demonstrates that it is statistical in (b)
(c) In this instance, the subject is not treated by the researcher.
The observational research is presented here.
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At a hair salon, each womab is charged $15 for a cut and 35$ for a color. how much money will the salon earn if w women grt a cut and a color?
=$50
Step-by-step explanation:
Total amount to be earn
if one women cut and add a colour
35$ + 15$
= $50
The salon earn if the women get a cut and a colour is $50.
What is Total amount?There are many meanings of total, but they all have something to do with completeness. A total is a whole or complete amount, and "to total" is to add numbers or to destroy something.
In math, you total numbers by adding them: the result is the total. If you add 8 and 8, the total is 16. If a car is totalled in an accident, it has been completely destroyed. A total defeat is a complete and utter defeat with no chance of recovering. The total resources of a company are all its resources, everything it has.
Step-by-step explanation:
Total amount to be earn
if one women cut and add a colour
35$ + 15$
= $50
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Use Descartes' Rule of Signs to determine the possible numbers of positive and negative real zeros.
Answer:
(a) Possible number(s) of positive real zeros: 3
(b) Possible number(s) of negative real zeros: 1
Step-by-step explanation:
Descartes' Rule of Signs tells us the maximum number of positive and negative roots.
Positive root case
[tex]f(x)=-3x^4+2x^3-x^2+9x+7[/tex]
As there are 3 sign changes, the maximum possible number of positive roots is 3.
Negative root case
[tex]\begin{aligned}f(x)&=-3(-x)^4+2(-x)^3-(-x)^2+9(-x)+7\\&=-3x^4-2x^3-x^2-9x+7 \end{aligned}[/tex]
As there is one sign change, the maximum possible number of negative roots is 1.
solve 2x=32 in 2 different ways
Answer:
1. 32 divided by 2 is 16
2. 2 x 16 = 36
Step-by-step explanation:
please help me as quick as possible
Answer:
try this
Step-by-step explanation:
3. Find the volume of a cone with radius 6 m and height 20 m
Answer: 753.98m³
Formula:V=πr2h3=π·62·203≈753.98224m³
The equation $x^2 + 6x + y^2 + 6y = 18$ represents a circle. What is its center?
Answer:
Center = (-3, -3)
Step-by-step explanation:
[tex](x-h)^2+(y-k)^2=r^2\\\\Center=(h,k)[/tex]
[tex]x^2+6x+y^2+6y=18\\(x^2+6x \,\,\,\,\,\,\,) + (y^2+6y\,\,\,\,\,\,\,)=18\\\\\frac{6}{2} =(3)^2=9\,\,\,\,\,\,\,\,\,\,\,\,\,\, \frac{6}{2}=(3)^2 =9\\\\(x^2+6x+9)+(y^2+6y+9)=18+9+9\\(x+3)^2+(y+3)^2=36\\\\Center=(-3,-3)[/tex]
please help
it's 10 class
Answer:
=58%
Step-by-step explanation:
If rate of 5.8% = 1 day
than ? = 10 days
therefore 10/1 × 5.8%
= 10 × 5.8
= 58%
To the nearest whole number
= 58%
A 21 oz bottle of a new soda costs $2.59. What is the unit rate, rounded to the nearest tenth of a cent ?
There are 7 1/5 groups of 2/5 in 3 do you agree with this statement show reasoning
The statement made by Diego is correct.
In order to determine the number of groups of 5/6 that are in 1, 1 would be divided by 5/6.
1 ÷ 5/6
= 1 x 6/5 = 6/5
6/5 is called an improper fraction because the numerator is greater than the denominator.
6/5 can also be rewritten as a mixed fraction. If it is rewritten as a mixed fraction, it becomes 1 1/5.
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Given question is incomplete , the complete question is given below:
Diego said that the awnser to the question "How many groups of 5/6 are in 1?" Is 6/5 or 1 1/5.Do you agree with his statement? Explain or show your reasoning.
The probability that a married man watches a certain television show is 0.4,
and the probability that a married woman watches the show is 0.5. The
probability that a man watches the show, given that his wife does, is 0.7.
Find the probability that
a. a married couple watches the show;
b. a wife watches the show, given that her husband does;
c. at least one member of a married couple will watch the show.
Answer:
a. The probability that a married couple watches the show can be calculated by multiplying the probabilities that each spouse watches the show:
P(Married couple watches the show) = P(Husband watches the show) * P(Wife watches the show) = 0.4 * 0.5 = 0.2
Step-by-step explanation:
b. The probability that a wife watches the show, given that her husband does, can be calculated using Bayes' theorem:
P(Wife watches the show | Husband watches the show) = P(Husband watches the show | Wife watches the show) * P(Wife watches the show) / P(Husband watches the show)
P(Wife watches the show | Husband watches the show) = 0.7 * 0.5 / 0.4 = 0.875
c. The probability that at least one member of a married couple will watch the show can be calculated as the sum of the probabilities that either the husband or the wife watches the show:
P(At least one member of a married couple watches the show) = P(Husband watches the show) + P(Wife watches the show) - P(Married couple watches the show) = 0.4 + 0.5 - 0.2 = 0.7
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
In April 1986, a flawed reactor design played a part in the Chernobyl nuclear meltdown. Approximately 14252 becqurels (Bqs), units of radioactivity, were initially released into the environment. Only areas with less than 800 Bqs are considered safe for human habitation.
The function f(x)=14252(0.5)^x/32 describes the amount, f(x) in becqurels of a radioactive element remaining in the area x years after 1988.
Find F(40) to one decimal place in order to determine the amount of becqurels in 2026.
The determine if the area is safe for human habitation in the year 2026.
(SAT Prep) Find the value of x.
20⁰
X
40°
The value of the angle is 120°.
What are Corresponding angle?The corresponding angle of a given angle refers to the angle in a congruent position in another figure. For example, if two lines intersect, the angle formed at one vertex of the intersection is called a vertex angle. The corresponding angle in the other figure is the angle in a congruent position, meaning that it has the same measure.
We are given two lines to be parallel
Hence the angle adjacent to x is 40°
Now Sum of All three angle is 180° (Angles in linear pair)
Hence we have
40 + x + 20 = 180°
x = 120°
Hence the measure of angle x is 120°
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please help!!
I can’t put the answer options because brainly won’t allow me to choose multiple photos at once, but there are solid line graphs, dotted line graphs, and they are all shaded.
How do i show my work?
well, let's take a looksie at both
[tex]~~~~~~ \stackrel{\textit{\LARGE Henry}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (5000)(0.042)(4) \implies I = 840 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\LARGE Ingrid}}{\textit{Simple Interest Earned}}[/tex]
[tex]I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 3.9\%\to \frac{3.9}{100}\dotfill &0.039\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (5000)(0.039)(6) \implies I = 1170 \\\\[-0.35em] ~\dotfill\\\\ 1170~~ - ~~840\implies \text{\LARGE 330}[/tex]
______ 6x 8/5
ITS FOR KHAN ACADAMEY HELP
6x8 is 48. You can't simplify 48/5, so that's your answer. If you wanted to create a mixed number, you could write 9 3/5
4232852 round off yo the nearest 1000
Answer:
4,233,000
Step-by-step explanation:
4,232,000 4,4232,852 4,233,000
4,4232,852 is between 4,232,000 and 4,233,000. It is closer to 4,233,000.
The rule is to look a the digit in the hundreds' place. That number is 8. If the digit in the hundreds' place is 5 or larger, you round up.
Question 2
Two fair six-sided dice are thrown. Let A be the event that the sum is 3. Let B be the event that the sum is 12.
Find P(AUB).
None of the answers listed is correct.
2/12
3/36
4/36
2/36
E1, E3, and E2, E3 are independent variables.
What is meant by independent variable?In statistical modelling, experimental sciences, and mathematical modelling, there are dependent and independent variables. Dependent variables are examined under the presumption or requirement that they are constrained by some rule or law to depend on the values of other variables. What it means to be an independent variable is exactly what it is. It is a variable that is independent of the other factors you are attempting to assess. Age is just one example of an independent variable.The independent variable is the underlying cause. Its value is independent of the other study factors. The dependent variable is the effect. The value of the independent variable depends on its modifications.[tex]$& \mathrm{P}\left(\mathrm{E}_1\right)=\frac{1}{6} \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_2\right)=\frac{1}{6} \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_3\right)=\frac{2+4+6+4+2}{36}=\frac{1}{2} \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_2 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_2\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]
Then,
[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_1\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right)=0 \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right) \equiv 0 \\[/tex]
Simplify,
[tex]$& \therefore \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right) \equiv \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right)[/tex]
E1, E3 are independent
E2, E3 are independent
The complete question is:
Let two fair six-faced dice A and B are thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?
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What is the image of (1, 0) after a dilation by a scale factor of 4 centered at the
origin?
Answer:
(4, 0)
Step-by-step explanation:
You want the image point coordinates of (1, 0) dilated by a factor of 4 centered at the origin.
DilationWhen the dilation is centered at the origin, all coordinate values are multiplied by the scale factor.
(1, 0) ⇒ 4(1, 0) = (4, 0)
The image of the point is (4, 0).
Find side RT
10 m
13m
14 m
16 m
The side RT of the triangle is 13 m.
How to find the side RT of the triangle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
The sine law is a mathematical formula used in trigonometry to relate the sides and angles of a triangle. The sine law states that:
a/sin(A) = b/sin(B) = c/sin(C)
where:
a, b, and c are the lengths of the sides of the triangle
A, B, and C are the angles opposite those sides
Using sine law:
RT/sin 34° = ST/sin 109°
RT/sin 34° = 22/sin 109°
RT = (22 * sin 34°)/(sin 109°)
RT = 13 m
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