Answers
Answer:
BC = 11.9Step-by-step explanation:
To solve for BC we use sine
sin ∅ = opposite / hypotenuse
From the question
AC is the hypotenuse
BC is the opposite
So we have
sin 58 = BC / AC
sin 58 = BC / 14
BC = 14 sin 58
BC = 11.87
BC = 11.9 to one decimal place
Hope this helps you
Answer:
[tex]\boxed{BC = 11.9 \ cm}[/tex]
Step-by-step explanation:
Sin A = [tex]\frac{opposite}{hypotenuse}[/tex]
Where A = 58°, Opposite = BC and AC = 14 cm
Sin 58 = [tex]\frac{BC}{14}[/tex]
BC = 0.848 * 14
BC = 11.9 cm
Related Questions
what is a measure ∠x
Answers
Answer:
x = 138
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
x = B+ C
x = 68+ 70
x =138
Answer:
138 degrees
Step-by-step explanation:
A triangle is made up of 180 degrees, it lists 2 values already, 68&70. when added that equals 138.
So 180-138 is 42 degrees, which would be the last angle within the triangle.
Since a line is also 180 degrees, its 180-42, which makes x 138 degrees
A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of miles and a standard deviation of miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?
Answers
Complete question is;
A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 34,000 miles and a standard deviation of 2500 miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?
Answer:
The mechanics worded guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.
Step-by-step explanation:
Let X = Life expectancy of the automobile tire
For the normal distribution, we are given;
μ = 34000
σ = 2700
Let y miles be the minimum miles of the tyres which the mechanic guarantees that he will replace if it's last less than that.
Now, since the mechanic is willing to replace approximately 10% of the tires, y would be such that:
P(X ≤ y) = 0.1
Using the z formula, we have;
P[(X - μ)/σ) ≤ [(y - μ)/σ] = 0.1
Thus;
P(Z ≤ ([y - μ]/σ) = 0.1
From z-distribution table the Z-score at 0.1 is approximately -1.2816
This is P(Z ≤ -1.2816)
Thus;
[y - μ]/σ = -1.2816
(y - 34000)/2500 = -1.2816
y - 34000 = -1.2816 × 2500
y - 34000 = -3204
y = 34000 – 3204
y = 30796
So, we conclude that the mechanic will guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.
Which expression is equivalent to x^2 • x^3?
Answers
Answer:
x^5
Step-by-step explanation:
x^2 . x^3
x^(2+3)
x^5
6 root 5 plus 6 root 5
Answers
Answer:
12√5
Step-by-step explanation:
6√5 + 6√5 = (6 + 6) * √5 = 12 * √5 = 12√5.
Answer:
12 [tex]\sqrt{5}[/tex]
Step-by-step explanation:
When you add the surds which are the same type, (both are root 5), just add the integers before them together.
An umbrella has 8 ribs which are equally spaced (see fig.). Assuming umbrellato
be a flat circle of radius 45 cm, find the area between the two consecutive ribs of
the umbrella.
Answers
Answer:
Yes.
Step-by-step explanation:
You are correct except to the nearest hundredth it is 795.54 cm^2.
In a school, 25% of the teachers teach basic math. If there are 50 basic math teachers, how many teachers are there in a school?
Answers
Answer:
200 teachers
Step-by-step explanation:
If 25% is a fourth of the teacher staff, and this value is fifty, to find out how many teachers there are you just have to multiply by 4 to find out the 100%. So this means that 50*4= 200
Answer:
Total teachers = 200
Step-by-step explanation:
Let x be the total teachers in school
Basic Maths teachers = 25 % of x
Basic Maths Teachers = 50
=> 25% of x = 50
=> [tex]\frac{25}{100} x = 50[/tex]
=> [tex]\frac{x}{4} = 50[/tex]
Multiplying both sides by 4
=> x = 200
The table shows the number of flowers in four bouquets and the total cost of each bouquet. A 2-column table with 4 rows. The first column is labeled number of flowers in the bouquet with entries 8, 12, 6, 20. The second column is labeled total cost (in dollars) with entries 12, 40, 15, 20. What is the correlation coefficient for the data in the table? –0.57 –0.28 0.28 0.57
Answers
Answer:
The correct option is;
0.28
Step-by-step explanation:
The given data values are;
x, f(x)
8, 12
12, 40
6, 15
20, 20
Where;
x = The number of flowers in the bouquet
f(x) = The total cost (in dollars)
The equation for linear regression is of the form, Y = a + bX
The formula for the intercept, a, and the slope, b, are;
[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]
[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]
Where:
N = 4
∑XY = 1066
∑X = 46
∑Y = 87
∑X² = 644
(∑X)² = 2116
b = (4*1066 - 46*87)/(4*644 - 2116) = 0.5696
a = (87 - 0.5696*46)/4 = 15.1996
The standard deviation of the x- values
[tex]S_X = \sqrt{\dfrac{\sum (x_i - \mu)^2}{N} }[/tex]
[tex]\sum (x_i - \mu)^2}[/tex] = 115
N = 4
Sx =√(115/4)
Sx = 5.36
[tex]S_Y = \sqrt{\dfrac{\sum (y_i - \mu_y)^2}{N} }[/tex]
[tex]\sum (y_i - \mu_y)^2}[/tex] = 476.75
N = 4
Sy =√(476.75/4)
Sy= 10.92
b = r × Sy/Sx
Where:
r = The correlation coefficient
r = b × Sx/Sy = 0.5696*5.36/10.92 = 0.2796 ≈ 0.28
The correct option is 0.28.
Answer:
C on edge
Step-by-step explanation:
A high school wants to sell postage stamps with the school logo on them. The fundraising group have purchased 500 sheets of stamps at $16/sheet plus $50 to create the image. They plan to sell each sheet for $20. a) Write an equation that represents the cost of obtaining the stamps. b) Write an equation that represents the income from sales. c) For each equation, set up a table of values. d) Graph each equation on the same set of coordinate axis. e) What is the minimum number of sheets the group must sell so they don't lose any money? f) How much profit will they make if they sell 500 sheets?
Answers
Answer:
a) Cost
[tex]C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050[/tex]
b) Sales income
[tex]S(q)=20q\\\\S(500)=20\cdot 500 = 10,000[/tex]
c) Table of values
[tex]\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right][/tex]
d) Attached
e) Breakeven point = 12.5 sheets
f) Profit at 550 sheets = $1,950
Step-by-step explanation:
a) We have a fixed cost for the image, at $50.
We also have a variable cost of $16 a sheet.
The purchased quantity is 500 sheets.
Then, the cost function is:
[tex]C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050[/tex]
b) The price for each sheet is $20, so the income from sales are:
[tex]S(q)=20q\\\\S(500)=20\cdot 500 = 10,000[/tex]
c) Table of values
[tex]\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right][/tex]
d) Attached
e) The minimum number of sheets the group must sell so they don't lose any money is the breakeven point (BEP) and can be calculated making the income sales equal to the cost:
[tex]S(q)=C(q)\\\\20q=50+16q\\\\(20-16)q=50\\\\4q=50\\\\q=50/4=12.5[/tex]
f) This profit can be calculated as the difference between the sales income and the cost:
[tex]P(500)=S(500)-C(500)\\\\P(500)=20\cdot 500-(50+16\cdot 500)=10,000-8,050=1,950[/tex]
The given number of 500 sheets of stamps purchased at $16/sheet with
a plan to sell each sheet for $20 gives the following values;
(a) Cost, C = 50 + 16·q
(b) Income, R = 20·q
(c) Please find the included table of values and the attached graph
(e) Approximately 403 sheets
(f) $1,950
Which method can be used to derive the equations?
(a) The cost per sheet of stamp = $16/sheet
The cost to create the image = $50
Amount at which they plan to sell each sheet, P = $20
Therefore
Cost of obtaining the stamps, C = 50 + 16·q(b) The income from sale, R = Number of units sold × P
Which gives;
R = 20·q(c) The table of values are therefore;
C = 50 + 16·q
[tex]\begin{array}{|c|c|c|}q&C=50+16 \times q\\0&50\\1&66\\2&82\\3&98\\4&114\\5&130\\6&146\\7&162\\8&178\\9&194\\10&210\\11&226\\12&242\\13&258\\14&274\end{array}\right][/tex]
R = 20·q
[tex]\begin{array}{|c|c|c|}q&R = 20 \times q\\0&0\\1&20\\2&40\\3&60\\4&80\\5&100\\6&120\\7&140\\8&160\\9&180\\10&200\\11&220\\12&240\\13&260\\14&280\end{array}\right][/tex]
Please find attached the required graph created with MS Excel
e) The minimum number of sheets the group must sell is given as follows;
The cost of the sheets purchased = 50 + 16 × 500
Which gives;
At point of profitability; Income = Cost
50 + 16 × 500 = 20·[tex]q_{min}[/tex]
[tex]q_{min} = \dfrac{50 + 16 \times 500}{20} =402.5 \approx \mathbf{403}[/tex]
The minimum number the sheets they must sell, [tex]q_{min}[/tex] ≈ 403 sheets(f) The profit made by selling 500 sheets is; 20·q - (50 + 16·q)
Where;
q = 500
Which gives;
20 × 500 - (50 + 16 × 500) = 1,950
The profit made from selling 500 sheet = $1,950
Learn more about graphs of functions here:
https://brainly.com/question/22150463
WILL MARK BRAINLIEST
Answers
Answer:
A
Step-by-step explanation:
Find the volume of the cuboid which length is 10cm, breadth is 8cm and height is 7cm. Who answers first gets brainliest answer
Answers
Answer:
560cm
Step-by-step explanation:
Volume = Length × Breadth × Height
= 10 × 8 × 7
= 560 cm³
Answer:
Step-by-step explanation:
Volume =length x breadth x height
10 x 8 x 7=560cm^3
Please answer this in two minutes
Answers
Answer:
20/29
Step-by-step explanation:
SOH CAH TOA
so its opposite/hyp...
20/29
is the answer
abby owns a square plot of land. she knows that the area of the plot is between 2200 and 2400 square meters. which of the following answers is a possible value for the side length of the plot of land?
Answers
Answer:
48
Step-by-step explanation:
The formula for the area of a square is A = s². Plug in each value and see if is in between 2200 and 2400.
A = s²
A = (46)²
A = 2116
A = s²
A = (48)²
A = 2304
A = s²
A = (50)²
A = 2500
A = s²
A = (44)²
A = 1936
The only value that fits in between 220 and 2400 is 48.
Give the digits in the tens place and the tenths place.
12.05
Answers
The digit in the tenths place is 0.
Identify the continuous data.
A. the time you take your dog for a walk each day
B. the temperature of the water in the local river during the day
C. how long it takes to run a lap around the track
D. the number of croutons in your daily salad
Answers
Answer:
A. The time you take your dog for a walk each day
B. The temperature of the water in the local river during the day
C. How long it takes to run a lap around the track
Step-by-step explanation:
Continuous data is quantitative data that you can measure. It can have an infinite number of possible values within a given range.
For example, you can measure times and temperatures to any number of decimal places if you have the appropriate equipment.
D is wrong. You can't measure the number of croutons in a salad. You must count them.
Help help help help help
Answers
for example with 4-6a
you would put 4 = 2•2 so 2 is it’s GCF
and 6= 3•2 so 3 is it’s GCF
however the question is asking for the combined GCF (meaning the whole problem)
so 4-6a’s GCF would be 2 considering it is the only greatest common factor between BOTH numbers
for 12a^2 - 8a you would use the same method:
12a^2= 3a•2a•2 and 3a is it’s GCF
8a = 2•2•2a and 2a is it’s GCF
but combined, the greatest factor BOTH numbers have in common is 2a, so 2a is the answer!
i hope i helped you :)!❤️
Find the missing side. Round your answer to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
In a right triangle, the sides forming the right angle also determine the angle opposite one of the sides.
Tan(29) =26/x Multiply both sides by x
x tan(29) = 26 Divide by tan(29)
x = 26/tan(29) Find tan(29)
x = 26/0.5543 Divide
x= 46.9
Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.
(–2, 0)
(–2, 0) and (2, 0)
(–2, 0) and (3, 5)
no solutions
Answers
Answer:
c
Step-by-step explanation:
c
Answer:
the answer is C ;D
Step-by-step explanation:
Help please!!!!!thxxxx
Answers
Answer:
144
Step-by-step explanation:
An angle of a regular pentagon is of 180(5-2)/5=108°
and that all the sides are equal so angle MNL=108/3=36
then MNK=180-MNL=180-36=144
I don't know if you understand this but it's hard to work without more points :)
How many 5-digit palindromes contain only even digits?
Answers
Answer:
400
Step-by-step explanation:
There are 400.
Assuming the number must be at least 10,000, then:
In a 5 digit palindrome, the first and last digits must be the same, and the second and fourth digits must be the same; and:
For the first and last digit there is a choice of 4 digits {2, 4, 6, 8};
For each of these there is a choice of 10 digits {0, 1, ..., 9} for the second and fourth digits;
For each of the above choices these is a choice of 10 digits {0, 1, ..., 9} for the third digit;
Making 4 x 10 x 10 = 400 possible even 5 digit palindromes.
Miriam is setting up a fishing game in a kiddie pool for her niece's birthday party. The pool has a circular base with a diameter of 4 feet and a height of 0.75 feet. She wants to fill the pool halfway so there is plenty of space left for the plastic fish. Approximately how many cubic feet of water does she need? 9.4 1.5 2.4 4.7
Answers
Answer:
4.7 feet³ of water
Step-by-step explanation:
Diameter of 4 feet
Radius = 2 feet
Height = 0.75 feet
Formula for Volume = 2·[tex]\pi[/tex]·radius·height
But she only wants to fill half, so divide by 2, cancels the 2 in the formula for volume, giving us: [tex]\pi[/tex]·radius·height
[tex]\pi[/tex]·2·0.75 = 4.71 feet³
At which value in the domain does f(x)=0? On a coordinate plane, a function goes through the x-axis at (negative 2.5, 0), (negative 0.75, 0), (0, negative 3), and (1, 0).
Answers
Answer:
The values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.
Step-by-step explanation:
Since we are given the points (-2.5,0), (-0.75, 0), (0, -3) and (1,0) where the coordinates are in ordered pairs of (x, y) where y = f(x).
To find the values in the domain where f(x) = 0, we look at the ordered pairs given.
We look for the pair in which f(x) = 0.
So f(x) = 0 in (-2.5, 0)
f(x) = 0 in (-0.75, 0)
and f(x) = 0 in (1, 0)
The corresponding values of x in which f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.
So, the values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.
Answer:
C. [tex]x=1[/tex]
Step-by-step explanation:
When x is 1, y is 0.
Question 7(Multiple Choice Worth 1 points)
(06.02 MC)
The radius of the cone is 5 in and y = 13 in. What is the volume of the cone in terms of n?
40nt in
43n in
O
100nt in
108n in
Answers
Hey there! I'm happy to help!
I assume that n is supposed to be π. To find the volume of a cone, you multiply the base by the height and then divide by three.
First, we find the area of the base, which is a circle. To find the area of a circle, you square the radius and multiply by π.
5²=25
And we multiply by π.
25π
Now we multiply by the height.
25π×13=325π
We divide by three.
325π/3≈108π
Therefore, the answer is 108π in.
Have a wonderful day! :D
Solve the following system using substitution.
Answers
Answer/Step-by-step explanation:
3. By substitution method, let's substitute [tex] \frac{2}{3}x- 4 [/tex] for y in the first equation.
Thus,
[tex] \frac{1}{3}x + 2(\frac{2}{3}x- 4) = 1 [/tex]
Solve for x
[tex] \frac{x}{3} + \frac{4x}{3} - 4 = 1 [/tex]
Add 4 to both sides
[tex] \frac{x}{3} + \frac{4x}{3} - 4 + 4 = 1 + 4 [/tex]
[tex] \frac{x}{3} + \frac{4x}{3} = 5 [/tex]
[tex] \frac{x + 4x}{3} = 5 [/tex]
[tex] \frac{5x}{3} = 5 [/tex]
Multiply both sides by 3
[tex] \frac{5x}{3}*3 = 5*3 [/tex]
[tex] 5x = 15 [/tex]
Divide both sides by 5
[tex] x = 3 [/tex]
Now, substitute 3 for x in the equation.
[tex] y = \frac{2}{3}x- 4 [/tex]
[tex] y = \frac{2}{3}(3) - 4 [/tex]
[tex] y = 2 - 4 [/tex]
[tex] y = -2 [/tex]
The solution of the equation is x = 3, y = -2
4. Solving by elimination, let's try to eliminate the x-variable by adding both equation together.
[tex] 3x - 2y = 11 [/tex]
[tex]-3x - y = 4[/tex]
[tex] -3y = 15 [/tex] => [tex] (-3x +(-3x) = 0; -2y +(-y) = -3y; 11 + 4 = 15) [/tex]
Divide both sides by -3 to solve for y
[tex] \frac{-3y}{-3} = \frac{15}{-3} [/tex]
[tex] y = -5 [/tex]
Substitute -5 for y in the first equation to find x
[tex] 3x - 2(-5) = 11 [/tex]
[tex] 3x + 10 = 11 [/tex]
Subtract 10 from both sides
[tex] 3x + 10 - 10 = 11 - 10 [/tex]
[tex] 3x = 1[/tex]
Divide both sides by 3
[tex] \frac{3x}{3} = \frac{1}{3} [/tex]
[tex] x = \frac{1}{3} [/tex]
The solution is [tex] x = \frac{1}{3}, y = -5 [/tex]
HELPPP!! Calculate the side lengths a and b to two decimal places. (there is a picture included)
Answers
Answer:
Option (D)
Step-by-step explanation:
In the given triangle ABC,
Sum of all interior angles = 180°
m∠A + m∠B + m∠C = 180°
72° + 85° + m∠C = 180°
m∠C = 180 - 157
m∠C = 23°
By applying Sine rule in the triangle,
[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{\text{SinC}}{c}[/tex]
[tex]\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=\frac{\text{Sin23}}{6.2}[/tex]
[tex]\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=0.06302[/tex]
[tex]\frac{\text{Sin72}}{a}=0.06302[/tex]
a = [tex]\frac{\text{Sin72}}{0.06302}[/tex] = 15.09
[tex]\frac{\text{Sin85}}{b}=0.06302[/tex]
b = [tex]\frac{\text{Sin85}}{0.06302}[/tex]
b = 15.81
Therefore, option (D) will be the answer.
Mr.lopez wrote the equation 32g+8g-10g=150
Answers
Answer:
g=5
Step-by-step explanation:
32g+8g-10g=150
30g=150
g=5
[tex]( \frac{1 + i}{1 - i} ) {}^{2} [/tex]
Please tell me the answer i need help
Answers
Answer:
- 1
Step-by-step explanation:
Given
( [tex]\frac{1+i}{1-i}[/tex] )²
= [tex]\frac{(1+i)^2}{(1-i)^2}[/tex]
= [tex]\frac{(1+i)(1+i)}{(1-i)(1-i)}[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{1+2i+i^2}{1-2i+i^2}[/tex] ← simplify using i² = - 1
= [tex]\frac{1+2i-1}{1-2i-1}[/tex]
= [tex]\frac{2i}{-2i}[/tex]
= - 1
What is the simplified form of y^2+7y+12/y^2-2y-15? Choices:
Answers
Answer:
[tex] \frac{y + 4}{y - 5} [/tex]Option C is the correct option
Step-by-step explanation:
[tex] \frac{ {y}^{2} + 7y + 12}{ {y}^{2} - 2y - 15 } [/tex]
Write 7y as a sum
[tex] \frac{ {y}^{2} + 4y + 3y + 12}{ {y}^{2} - 2y - 15} [/tex]
Write -2y as a difference
[tex] \frac{ {y}^{2} + 4y + 3y + 12}{ {y}^{2} + 3y - 5y - 15} [/tex]
Factor out y from the expression
[tex] \frac{y(y + 4) + 3y + 12}{ {y}^{2} + 3y - 5y - 15 } [/tex]
Factor out 3 from the expression
[tex] \frac{y(y + 4) + 3(y + 4)}{ {y}^{2} + 3y - 5y - 15 } [/tex]
factor out y from the expression
[tex] \frac{y(y + 4) + 3(y + 4)}{y(y + 3) - 5y - 15} [/tex]
Factor out -5 from the expression
[tex] \frac{y(y + 4) + 3(y + 4)}{y(y + 3) - 5( y + 3)} [/tex]
factor out y + 4 from the expression
[tex] \frac{(y + 4)(y + 3)}{y(y + 3) - 5(y + 3)} [/tex]
Factor out y + 3 from the expression
[tex] \frac{(y + 4)(y + 3)}{(y + 3)(y - 5)} [/tex]
Reduce the fraction with y + 3
[tex] \frac{y + 4}{y - 5} [/tex]Hope this helps..
Best regards!!
If the m1 = 40, what is the m 3
Answers
Explanation:
m1 = 40
m3 = 40 x 3
m3 = 120
Answer:
Your Answer is 120Step-by-step explanation:
m1=40
Taking m3
m3=40 ×3
m3= 120
Hope It helps UIn a fiftness class, there was a warm up of 14 press-ups. Anyone unable to do 14 or more recives a punishment. Jessica can do 10 press-ups without ever failing, however, the chances of her successfully doing each subsequent press-up halves. Whats the probality of her receiving a punishment? A. 1 in 8 B. 1 in 1024 C. 15 in 16 D. 1023 in 1024
Answers
Answer:
The correct option is;
C. 15 in 16
Step-by-step explanation:
The given information are;
The number of press-ups required = 14 press-ups
The number of press-ups Jessica is sure to do = 10 press-ups
The chance of Jessica doing subsequent press-ups after 10 halves each time
The consequence of not completing the 14 press-ups = Punishment
The probability that Jessica does goes on to do 11 press-ups = 1/2
The probability that Jessica does goes on to do 12 press-ups = 1/2×1/2
The probability that Jessica does goes on to do 13 press-ups = 1/2×1/2×1/2
The probability that Jessica does goes on to do (completes) 14 press-ups = 1/2×1/2×1/2×1/2 = 1/16
Therefore;
Since the probability that Jessica does not receive a punishment because she completed the 14 push-ups is 1/16, we have;
The probability that Jessica does not complete the 14 press-ups and receives a punishment = 1 - 1/16 = 15/16 which is 15 times out of 16 or 15 in 16.
Please answer this question now
Answers
Answer:
[tex] Area = 538.5 m^2 [/tex]
Step-by-step Explanation:
Given:
∆XVW
m < X = 50°
m < W = 63°
XV = w = 37 m
Required:
Area of ∆XVW
Solution:
Find side length XW using Law of Sines
[tex] \frac{v}{sin(V)} = \frac{w}{sin(W)} [/tex]
W = 63°
w = XV = 37 m
V = 180 - (50+63) = 67°
v = XW = ?
[tex] \frac{v}{sin(67)} = \frac{37}{sin(63)} [/tex]
Cross multiply
[tex] v*sin(63) = 37*sin(67) [/tex]
Divide both sides by sin(63) to make v the subject of formula
[tex] \frac{v*sin(63)}{sin(63)} = \frac{37*sin(67)}{sin(63)} [/tex]
[tex] v = \frac{37*sin(67)}{sin(63)} [/tex]
[tex] v = 38 [/tex] (approximated to nearest whole number)
[tex] XW = v = 38 m [/tex]
Find the area of ∆XVW
[tex] area = \frac{1}{2}*v*w*sin(X) [/tex]
[tex] = \frac{1}{2}*38*37*sin(50) [/tex]
[tex] = \frac{38*37*sin(50)}{2} [/tex]
[tex] Area = 538.5 m^2 [/tex] (to nearest tenth).