Answer:
x^2-23
Step-by-step explanation:
For what value of a the distance between the points 2 3 and 5 A is equal to 5?.
For a = 1 and a = -7, the distance between the points (2, -3) and (5, a) is equal to 5.
As we know according to the distance formula the distance between points (x₁, y₁) and (x₂, y₂) is given by,
[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]
Here we have been given the distance between the points (2, -3) and (5, a)
Let us assume that (x₁, y₁) = (2, -3)
and (x₂, y₂) = (5, a)
Let d represents the distance between points (2, -3) and (5, a)
here d = 5 units
Using above distance formula,
[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow 5 = \sqrt{(5 - 2)^2 + (a -(- 3))^2}\\\\\Rightarrow 5 = \sqrt{(3)^2 + (a+3)^2}\\\\\Rightarrow 5^2=(3)^2 + (a+3)^2\\\\\Rightarrow 25=9+(a+3)^2\\\\\Rightarrow (a+3)^2=16\\\\\Rightarrow a+3=\pm 4[/tex]
⇒ a + 3 = 4 OR a + 3 = -4
⇒ a = 4 - 3 OR a = -4 - 3
⇒ a = 1 OR a = -7
Therefore, the values of 'a' are 1, -7
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The complete question is
For what value of a the distance between the points (2, -3) and (5, a) is equal to 5?.
Phill baked two kind of pie. Each pie pan wa the ame ize. He erved 1/2 of blueberry and 1/4 of apple pie. If each pie had 8 piece to tart what fraction in eighth of the apple pie did he erve? how many more piece of the blueberry pie than apple did he erve
[tex]\frac{2}{8}[/tex] fraction of the apple pie was served.
Two more pieces of the blueberry pie were served than the apple pieces.
Given that,
Both blueberry pie and apple pie were divided into 8 equal parts each.
To compute the fraction in eights of apple pie, we do a multiplication of the current fraction with 8 parts:
1 apple pie=8 pieces of apple pie
1/4 apple pie = [tex]\frac{1}{4}[/tex] * 8 pieces of apple pie = 2 pieces of apple pie.
1 blueberry pie=8 pieces of blueberry pie.
1/2 blueberry pie = [tex]\frac{1}{2}[/tex] * 8 pieces of blueberry pie = 4 pieces of apple pie.
Thus. 1/4 apple pie is 2 pieces out of 8 pieces of apple pie or written as [tex]\frac{2}{8}[/tex] a fraction of apple pie.
And they served blueberry pies are 4 pieces but served apple pies are 2 pieces, thus the count of pieces of blueberry pie is 2 more than the count of pieces of apple pie served.
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I need some help on this question
The value of x is 39 and the values of angle m1 and m2 is 63 and 117. We can solve the question using linear pair.
What is linear pair?
When two lines meet at a single point, a pair of linear angles is created. If the angles follow the point where the two lines cross, they are considered to be linear pair. A linear pair's angles add up to 180° in every case. These angles are additionally referred to as. Angles with a shared vertex are those that are adjacent.
Therefore, the linear angles also have a common vertex in this instance.
Additionally, a common arm that symbolizes both angles will be present.
A ladder against a wall that creates linear angles at the ground is an example of a linear pair in real life. One who is straight is represented by linearity.
Using linear pair, we have equation
m1 +m2 = 180
x+24 +3x = 180
4x = 156
x = 39
Then the values of m1 =x +24 = 64
m2 = 3x = 117
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Jack bought 25 yard of fabric for $75. How much would 96 yard of the ame fabric cot? What i the rate of the fabric per yard?
96 yards of the same fabric would cost 288$ and the rate of the fabric per yard is 3$
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
No. yards = 25 yardsTotal cost = $75No. yards 2 = 96 yardsCost (96 yards) = ?Rate = ?Calculating the rate of the fabric per yard we have:
Rate = total cost / No. yards
Rate = $75 / 25 yard
Rate = $3 per yard
Calculating the amount of dollars paid for 96 yards:
Cost (96 yards) = No. yards 2 * Rate
Cost (96 yards) = 96 yards * 3$/ yard
Cost (96 yards) = 288$
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Find a principal which will amount to Rs.2000 in 6 years 8 months at the rate of interest 5% per annum.
Answer:
1449.28
Step-by-step explanation:
To find the principal amount that will amount to Rs. 2000 in 6 years 8 months at a 5% interest rate per annum, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A = final amount
P = principal (the amount we are trying to find)
r = interest rate per annum (in decimal form)
n = number of times interest is compounded per year
t = time in years
In this case, the final amount is Rs. 2000, the interest rate is 5% per annum (or 0.05 in decimal form), the number of times interest is compounded per year is 1 (since the interest is compounded annually), and the time is 6 years 8 months (or 6.67 years in decimal form).So we can substitute these values into the formula and solve for P:
2000 = P (1 + 0.05)^(1 * 6.67)
To solve this equation, we can use a calculator or a spreadsheet to calculate the right side of the equation: (1+0.05)^6.67 = 1.382000 = P * 1.38
P = 2000/1.38
P = 1449.28
The principal amount that will amount to Rs. 2000 in 6 years 8 months at a rate of interest of 5% per annum is Rs. 1281.97.
The principal amount (P) that will amount to Rs. 2000 in 6 years 8 months at the rate of interest of 5% per annum can be calculated using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal
r = rate of interest (5% per annum = 0.05)
n = number of times the interest is compounded per year (e.g. annually, semi-annually, quarterly)
t = time in years (6.67 years = 6 years 8 months)
Let's assume n = 12 (monthly compounding)
Substituting the values into the formula, we get:
2000 = P(1 + 0.05/12)^(12*6.67)
(To solve for P, we can divide both sides of the equation by the right side of the equation)
P = 2000 / (1 + 0.05/12)^(12*6.67)
P ≈ Rs. 1281.97
Therefore, the principal amount that will amount to Rs. 2000 in 6 years 8 months at a rate of interest of 5% per annum is Rs. 1281.97
It's important to note that this calculation is based on the assumption that the interest is compounded monthly, if the interest is compounded annually or semi-annually the amount will be different.
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Mitchell and his friends go out to eat at Perfect Slice Pizzeria.They order to large pizzas to share.Each large pizzas has 16 slices.Mitchell and friends split it between the 8 of them
The slices that each person gets from the 16 slices of pizza will be 2 slices.
How to calculate the word problem?It should be noted that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, Mitchell and his friends go out to eat at Perfect Slice Pizzeria and order to large pizzas that has 16 slices.
The slices that each person gets from the 16 slices of pizza will be:
= 16 / 8.
= 2 slices.
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Complete question
Mitchell and his friends go out to eat at Perfect Slice Pizzeria.They order to large pizzas to share.Each large pizzas has 16 slices.Mitchell and friends split it between the 8 of them. How many slices will each person get?
Eddie and Ellen use a calculator to work out
Eddie's answer is 1.5
Ellen's answer is 15
One of those answers is correct.
431.1/ 14.3 +3.8²2
Use approximations to find out which answer is correct.
Answer: 14.3 times 1.5 equals 55.
Step-by-step explanation: multiplication can be used to solve the equation
can someone explain how 1x-0.30x=0.7x
i just need an explanation ty
Answer:
See attached
Step-by-step explanation:
You can write 1 as 1.00 then line up the decimals with0.30 and subtract. The answer will be .7 or 0.7. They mean the same thing.
Helpppp please..
Solve the system of linear equations by graphing
y=-x+7
y=x+1
Answer: (3, 4)
Step-by-step explanation: Hello! To do this, you have to substitute one of the equations into the other. You know that in the first equation, y = -x + 7. Substitute -x+7 for y in the second equation. You now have -x + 7 = x + 1. Add x to both sides of the equation. -x + 7 + x = x + x + 1. You now have 7 = 2x + 1. Subtract 1 from both sides of the equation. You now have 6 = 2x. Divide both sides of the equation by 2. You now have 3 = x. The x-coordinate of where both linear equations intersect is 3. (3, y).
You now have to solve for the y-coordinate. To do this, look at your given equations. Subtract 2 from both sides of the second equation. You now have y - 1 = x. Substitute y-1 for x in the first equation. You now have y = -(y - 1) + 7. Simplify to get y = -y + 1 + 7. Add y to both sides of the equation. y + y = -y + y + 1 + 7. You now have 2y = 1 + 7. Add 1 + 7 to get 2y = 8. Divide both sides by 2 to get y = 4. You now know that the x-coordinate where both linear equations intersect is 3, and you know that the y-coordinate where both linear equations intersect is 4. Your answer is in the format of (x, y), which is (3, 4).
3. Ura Snob has three times as many dimes as quarters. If he has $2.75, how many quarters
does he have?
Answer:
75x = 300
x = 4
So he has
4 quarters
3x = 3*4 = 12 dimes
4x = 4*4 = 16 nickels
Step-by-step explanation:
Which of the following points would be on the line x=7
Answer:
Step-by-step explanation:
You haven’t given the points mentioned. (-4 6) is a point on the line. slope-intercept equation of the line: y=7x+34 (0,34) is a point on the line.
2(3b+6) =78 : Answer is 11
-2(6c-3) = -72 : Answer is 6.5
Check left Side of both equations
Solve each equation in steps:
2(3b + 6) =78 Given3b + 6 = 39 Divide both sides by 23b = 33 Subtract 6 from both sidesb = 33/3 Divide by 3b = 11 Answer-2(6c - 3) = -72 Given6c - 3 = 36 Divide both sides by - 26c = 39 Add 3 to both sidesc = 39/6 Divide by 6c = 6.5 AnswerAnswer:
b = 11 c = 6.5Step-by-step explanation:
1) 2(3b + 6) = 78, value of b?
→ 2(3b + 6) = 78
→ 6b + 12 = 78
→ 6b = 78 - 12
→ 6b = 66
→ b = 66/6
→ [ b = 11 ]
Hence, the value of b is 11.
2) -2(6c - 3) = -72, value of c?
→ -2(6c - 3) = -72
→ -12c + 6 = -72
→ -12c = -72 - 6
→ -12c = -78
→ c = (-78)/(-12)
→ c = 78/12
→ [ c = 6.5 ]
Hence, the value of c is 6.5.
You are placing a fountain in a triangular koi pond. You want the
fountain to be the same distance from each edge of the
pond. Where should you place the fountain? Explain
your reasoning. Use a sketch to support your answer.
As the person wanted the fountain to be the same distance from each edge of the pond and the incenter of the triangle is equidistant
How to illustrate the distance?From the information, the person is placing a fountain in a triangular koi pond and want the fountain to be the same distance from each edge of the
pond.
The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. It can be thought of as the intersection of the triangle's internal angle bisectors. The fountain is equally spaced from each edge of the pond because the person wanted it to be, and the triangle's incenter is also evenly spaced.
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What is the standard form of Y =- 2x 5?.
The standard form of the line is Ax + By + C = 0 or we can say y = mx + c.
Equation of Line Point-slope form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.Slope-intercept form: y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).Standard form: Ax + By = C, where A and B are the x and y coefficients, respectively, and C is a constant.Intercept form: x/a + y/b = 1, where a and b are the x and y intercepts, respectively.Two-point form: (x - x1)/(x2 - x1) = (y - y1)/(y2 - y1), where (x1, y1) and (x2, y2) are two points on the line.Parametric form: x = x0 + at, y = y0 + bt, where x0, y0 are the coordinates of a point on the line and a, b are the direction ratios and t is a parameter.Normal form: (x - x0)nx + (y - y0)ny = 0, where (x0, y0) is a point on the line and nx, ny are the direction ratios of the line's normal vector.To know more about the equation of a line on brainly : brainly.com/question/21511618
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Your buine ha decided to tart recycling paper product. In exchange, the recycling company will donate 20 boxe of new paper each year to your buine. You currently order 150 boxe of paper per year, at $50 per box. If you tart recycling with the company, how much money will you ave each year?
You will save as much as $1000 each year if you start recycling with the company.
If your current order of 150 boxes of paper per year costs $50 per box, and in exchange of starting recycling with the company, the recycling company will donate 20 boxes of new paper each year to your business, then you will save as much as $1000 each year.
Determine how much you will save by multiplying the amount of boxes of paper the recycling company will give to your business with the cost of each box of paper.
20 boxes of new paper x $50 per box = $1000
Therefore, the amount you will save if you start recycling with the company will be as much as $1000 each year .
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Is Y =- 3 a horizontal line?.
So, Y = -3 is not a horizontal line but a vertical line.
A horizontal line is a line that runs along the x-axis and has a constant y-value. In the equation of a line, y = mx + b, a horizontal line has a slope of zero (m = 0) and a y-intercept of the constant value (b = constant).
The equation Y = -3 is not a horizontal line. This is an equation of a vertical line, which is a line that runs along the y-axis and has a constant x-value. In this case, the constant x value is -3.
A vertical line has no slope since it does not change in the x direction. The x-value is constant, which means the slope is undefined.
In a graph, a horizontal line can be represented by a straight line that is parallel to the x-axis, while a vertical line is represented by a straight line that is parallel to the y-axis.
To summarize, Y = -3 is not a horizontal line but a vertical line, which means that all the points on this line have the same x-coordinate (-3) and can take any value for y.
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Find the Maximum on the interval {3,5} for the line y= 2x+1
The maximum value of the linear equation on the given interval is:
y = 11
How to find the maximum on the given interval?We want to find the maximum of the linear function:
y = 2x + 1
On the interval [3, 5]
Notice that we have a line with a positive slope, thus, this is an increasing line.
Then the maximum is just what we get when we evaluate the function on the maximum value of the interval:
y = 2*5 + 1
y = 10 + 1
y = 11
The maximum value is 11.
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How are log and exponential functions inverse?.
Logarithm and exponential functions are inverse as log(ex)=x and elogx=x.
Knowing that logarithms were once a tool for multiplication when ships employed celestial navigation may be helpful to the layperson. The product of two numbers' logarithms is equal to the total of their individual logarithms. Numerous log tables were published and utilized mechanically.
In 1958, this was an excellent supplemental math topic. The slide rule converts multiplication to addition of lengths using one axis graphs of an exponential function and a graphic log table as a physical correlate. As a result, the logarithm of a product is equal to the sum of the logarithms of its components.
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The Tanners are installing a rectangular pool in their back yard. They are also enclosing the yard and pool with a fence and the back of their house. See the figure below. What is the minimum number of feet of fencing needed to enclose the yard?
He need a fence that is 54 feet long.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Area of rectangle is A = a*b
Consider the length to be 40 feet, which is how long one side of the yard is known to be. The yard's size is 280 square feet, as you are already aware. Knowing the yard's width is necessary in order to calculate the perimeter:
A = LW
W= 280/40 = 7 feet
The two 7-foot sides and one 40-foot side are fenced in by him . He,
therefore, He needs a fence that is 54 feet long.
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The difference between three times a number and four is seventeen
100 points
What is the equation for the line in slope-intercept form?
Answer: The answer would be y = −4x − 5
Step-by-step explanation: I hope this helps!
How do you sketch the graph of a function of two variables?.
A two-variable function's graph can be thought of as a surface in three dimensions.
The points (x, y, f(x, y)) where x and y are in the domain make up the graph of z=f(x, y). You can fine-tune the shape of the surface by drawing the curve k=f(x, y) in the plane z=k for different values of k. For instance, we're trying to comprehend the graph of z=f(x, y)=x2+y2. Keep in mind that k=f(x, y) is a circle for k>0 and since 0=x2+y2 implies that x=y=0.
Additionally, it is symmetric in relation to the z axis. We have a parabola for x=k or y=k. As a result, the graph represents the revolution of the parabola z=x2 over the z axis (see Thomas, math).
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Someone help me pleaseeee
For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.
What is right triangle?A right triangle, right-angled triangle, or more formally an orthogonal triangle—previously known as a rectangled triangle—is a triangle with one angle that is a right angle (i.e., a 90-degree angle), meaning that two of its sides are perpendicular. The foundation of trigonometry is the relationship between the sides and other angles of a right triangle.
The hypotenuse is the side that faces the right angle (side c in the figure). Legs are the sides that are next to the right angle (or catheti, singular: cathetus). Side a can be thought of as the side that is adjacent to angle B and opposite to (or opposite) angle A, whereas side b is the side that is adjacent to angle A and opposite to angle B.
Given a right triangle with base = 8 and an angle = 24°
Using angle sum property of triangle
24 + 90 + angle L = 180
L = 66°
Using Sohcahtoa
Tangent: tan(θ) = Opposite / Adjacent
tan(24°) = LK/8
0.445 = LK/8
LH = 8 × 0.445
LK = 3.56
LM = [tex]\sqrt{MK^2 + LK^2}[/tex]
LM = [tex]\sqrt{8^2 + 3.56^2}[/tex]
LM = 8.75
Thus, For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.
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¿Cuáles son las medidas de un cilindro (altura, radio) si su volumen es 500 cm3
The dimensions of the cylinder are -
{r} = √500/πh
{h} = (500/r²)
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the volume of the cylinder as -
V = 500 cm³
We can write -
V = 500
So, we can write -
πr²h = 500
So, we can write -
{r} = √500/πh
{h} = (500/r²)
Therefore, the dimensions of the cylinder are -
{r} = √500/πh
{h} = (500/r²)
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{Question in english -
What are the measurements of a cylinder (height, radius) if its volume is 500 cm3}
solve for N.
40 = 5n
Answer:
n=8
Step-by-step explanation:
40=5n
40=5x8
Answer:n=8 I hope this helps mark brainlist if correct
Step-by-step explanation:
40=5n
Swap the sides of the equation
5n=40
Divide both sides of the equation by 8
n=8
What is the formula of the range Mcq?.
The range formula determines the difference between the highest and the lowest values in a given set of numbers.
The range formula is mostly used in statistics where the range is the spread of the numbers or data from the lowest to the highest value and it is commonly used in variability. Let's learn more about the range formula and solve a few examples.
The range formula is highly used in statistics to consider the range given in a particular data set. The formula assists in determining the center of the set by finding the difference between the lowest and the highest number. In distribution, the big range means more variability whereas the less range means low variability. The range formula has the other aspects of statistics such as mean, median, and mode. Therefore, the formula to calculate the range is:
R = Highest Value (H) - Lowest Value (L)
Range Formula
R = H - L
In this context,
R is the range
H is the highest value
L is the lowest value
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Answer:
Step-by-step explanation:
The range formula determines the difference between the highest and the lowest values in a given set of numbers. The range formula is mostly used in statistics where the range is the spread of the numbers or data from the lowest to the highest value and it is commonly used in variability. Let's learn more about the range formula and solve a few examples.
The range formula is highly used in statistics to consider the range given in a particular data set. The formula assists in determining the center of the set by finding the difference between the lowest and the highest number. In distribution, the big range means more variability whereas the less range means low variability. The range formula has the other aspects of statistics such as mean, median, and mode. Therefore, the formula to calculate the range is:
R = Highest Value (H) - Lowest Value (L)
Range Formula
R = H - L
In this context,
R is the range
H is the highest value
L is the lowest value
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Please help, 25 points.
Answer:
Elena's calculator is not broken.
Step-by-step explanation:
0.06 x 0.5
You can also do this by ignoring the decimals and multiplying normally.
6 x 5 = 30
Then you you count the decimal places and start at the end of your product and move the number of decimal places to the left.
0.030 or 0.03
Equations with variables on both sides
Solve for f.
−ƒ +2 +4ƒ = 8 – 3ƒ
spara
2:
Back to task
Calculate the coordinates of the midpoint of point P and point Q, which are
shown below.
12
11
10
9
8
7
65
Calculator
Bookwork code: J44 not allowed
6
5-
43
3
2-
1
P
Q
#I
0 1 2 3 4 5 6 7 8 9 10 11 12
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In the coordinate plane, if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points are ({4 + 8}/2, {2 + 6}/2) = (12/2, 8/2) = (6, 4).
What is midpoint?Midpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of a line, and the midpoint is lying in between the two points. The midpoint divides the line joining these two points into two equal halves. Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.
The midpoint formula is used to find the midpoint between two points whose coordinates are known to us. The midpoint formula is also used to find the coordinates of the endpoint if we know the coordinates of the other endpoint and the midpoint. In the coordinate plane, if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points are ({4 + 8}/2, {2 + 6}/2) = (12/2, 8/2) = (6, 4). Let us learn more about the formula of the midpoint, and different methods to find the midpoint of a line.
(3, 8 )
given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
(x+x /2 ,y+y/2 )
here (x₁, y₁ ) = P (1, 6 ) and (x₂, y₂ ) = Q (5, 10 ) , then
midpoint = (1+5/2 ,++10/2 ) = ( 6/2 , 16/2 ) = (3, 8 )
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c = 21 km, a = 18 km, m B = 121° Find b
The value of the side b of the triangle is 33.8.
What is the sine angle rule?The following is a detailed explanation of the sine law: In a triangle, side "a" divided by angle sine "a" equals side "b" divided by angle sine "b" equals side "c" divided by angle sine "c." In order to determine the triangle's unknown lengths or angles, we apply the sine rule.
Given that the sides and angles are c = 21 km, a = 18 km, mB = 121°. The value of the side b will be calculated as,
b² = c² + a² -2accosB
b² = ( 21² ) + ( 18 )² - 2 x 21 x 18 x cos(121)
b² = 441 + 324 _ ( 756 x -0.5 )
b² = 441 + 324 + 378
b = √ ( 1143 )
b = 33.8
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