Use triangle ABC drawn below & only the sides labeled. Find the side of length AB in terms of side a, side b & angle C only. You will need to use both Soh-Cah-Toa and the Pythagorean Theorem to solve for side AB.
Answers
Answer:
[tex]AB = \sqrt{a^2 + b^2-2abCos\ C}[/tex]
Step-by-step explanation:
Given:
The above triangle
Required
Solve for AB in terms of a, b and angle C
Considering right angled triangle BOC where O is the point between b-x and x
From BOC, we have that:
[tex]Sin\ C = \frac{h}{a}[/tex]
Make h the subject:
[tex]h = aSin\ C[/tex]
Also, in BOC (Using Pythagoras)
[tex]a^2 = h^2 + x^2[/tex]
Make [tex]x^2[/tex] the subject
[tex]x^2 = a^2 - h^2[/tex]
Substitute [tex]aSin\ C[/tex] for h
[tex]x^2 = a^2 - h^2[/tex] becomes
[tex]x^2 = a^2 - (aSin\ C)^2[/tex]
[tex]x^2 = a^2 - a^2Sin^2\ C[/tex]
Factorize
[tex]x^2 = a^2 (1 - Sin^2\ C)[/tex]
In trigonometry:
[tex]Cos^2C = 1-Sin^2C[/tex]
So, we have that:
[tex]x^2 = a^2 Cos^2\ C[/tex]
Take square roots of both sides
[tex]x= aCos\ C[/tex]
In triangle BOA, applying Pythagoras theorem, we have that:
[tex]AB^2 = h^2 + (b-x)^2[/tex]
Open bracket
[tex]AB^2 = h^2 + b^2-2bx+x^2[/tex]
Substitute [tex]x= aCos\ C[/tex] and [tex]h = aSin\ C[/tex] in [tex]AB^2 = h^2 + b^2-2bx+x^2[/tex]
[tex]AB^2 = h^2 + b^2-2bx+x^2[/tex]
[tex]AB^2 = (aSin\ C)^2 + b^2-2b(aCos\ C)+(aCos\ C)^2[/tex]
Open Bracket
[tex]AB^2 = a^2Sin^2\ C + b^2-2abCos\ C+a^2Cos^2\ C[/tex]
Reorder
[tex]AB^2 = a^2Sin^2\ C +a^2Cos^2\ C + b^2-2abCos\ C[/tex]
Factorize:
[tex]AB^2 = a^2(Sin^2\ C +Cos^2\ C) + b^2-2abCos\ C[/tex]
In trigonometry:
[tex]Sin^2C + Cos^2 = 1[/tex]
So, we have that:
[tex]AB^2 = a^2 * 1 + b^2-2abCos\ C[/tex]
[tex]AB^2 = a^2 + b^2-2abCos\ C[/tex]
Take square roots of both sides
[tex]AB = \sqrt{a^2 + b^2-2abCos\ C}[/tex]
Related Questions
FREE GIFTCARD/ROBUX GIVE AWAY FOR RIGHT ANSWERS ONLY
GUYS PLEASE HURRY I NEED HELP
graph each figure with the given vertices and identify the figure. Then find the perimeter and area of the figure
1. S(0,0), T(3,-2), U(8,0)
2. 0(3,2), P(1,2), Q(1,-4), R(3,-4)
Answers
JUST PUT THE FREAKING POINTS ON THE GRAPH
Answer:
put the stuff on 1 to the first graph
Step-by-step explanation:
putt the stuff on 2 in the second one
Kirsty counts number of peas in a pod
Answers
Answer:
I do not know
Step-by-step explanation:
You need to put the rest of the question there so that we know how many peas there are and what is happening to the peas.
Answer:
Put the rest of the equation so we can help you
Step-by-step explanation:
-9x=36
What is the value of x?
Answers
Answer:
x = 16 because if you multiply that and then divide
Answer: x=-4
Step-by-step explanation:
-9x=36
Divide both sides by -9 to get x alone
x=-4
2r + 2 = 10
r=?
Hurry Please!!
Answers
Answer:
2r+2=10
Step-by-step explanation:
R is 4
u would do 2*4
that equals 8
next add 2+8
you get 10
Charlie saves $29.85 each month for 6 months. In the seventh month, he only saves $10.20. How much money will Charlie have saved after 7 months
Answers
Answer:
charli from tiktok???? RENAGADEEEEE
jk $40.05 is the answer
A turntable has a diameter of 40 cm what its circumference
Answers
Answer:
Circumference of turntable is 125.6 cm
Step-by-step explanation:
Diameter of turntable = 40 cm
We need to find circumference of turntable.
The formula used to calculate circumference is: [tex]Circumference=2\pi r[/tex]
where r is radius
We know that: [tex]radius=\frac{diameter}{2}[/tex]
Finding radius first:
[tex]radius=\frac{diameter}{2}\\radius=\frac{40}{2}\\radius = 20 \ cm[/tex]
So, radius r=20 cm
Now finding circumference
[tex]Circumference=2\pi r\\Circumference=2\times3.14\times20\\Circumference=125.6 \ cm[/tex]
So, circumference of turntable is 125.6 cm
The graph shows the number of miles Peter's car traveled and the gallons of gas used.
MILEAGE OF PETER'S CAR
160
140
120
100
Miles Traveled
80
60
40
20
8
9 10
1 2 3 4 5 6 7
Gallons of Gas
Which equation can be used to find the distance in miles, d, that the car can travel on g gallons of gas?
Answers
Answer:
I believe it’s d=16g
Step-by-step explanation: Because the graph is on 160 but we are converting it to a bigger number or smaller so it’s 16 I think
What is the quotient of the problem 0.492 : 0.04
Answers
Pls help will mark brainliest
Answers
Answer:
f(5) = 9
Step-by-step explanation:
f(x) = 4x - 11
f(5)
f(5) = 4(5) - 11 Substitute 5 for x
f(5) = 20 - 11 Solve down
f(5) = 9
Hope this helps!
Vertical angles are:
Always congruent
Sometimes congruent
Never congruent?
Answers
Answer:
always
Step-by-step explanation:
bc it’s right lolz
How many numbers have an absolute of 5/4
Answers
A4
Step-by-step explanation:
1/2
1/3
1/5
1/4
The numbers which have an absolute of 5/4 are; -5/4 and 5/4.
According to the question;
We are required to determine how many numbers have an absolute of 5/4.The absolute value of any number, a or -a is always positive a.
In essence, only numbers (-5/4) and 5/4 have an absolute of 5/4.
Read more;
https://brainly.com/question/12928519
Solve x2 - 16 = 59. What does x
equal?
Answers
Answer:
37.5
Step-by-step explanation:
Answer: x = 75/2 = 37.5
Step by Step:
Solve for x:
2 x - 16 = 59
Hint: | Isolate terms with x to the left hand side.
Add 16 to both sides:
2 x + (16 - 16) = 16 + 59
Hint: | Look for the difference of two identical terms.
16 - 16 = 0:
2 x = 59 + 16
Hint: | Evaluate 59 + 16.
59 + 16 = 75:
2 x = 75
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 2 x = 75 by 2:
(2 x)/2 = 75/2
Hint: | Any nonzero number divided by itself is one.
2/2 = 1:
Answer: x = 75/2 = 37.5
I don't understand this question, help me, someone, please
Answers
Answer:
Arranging the terms from least to greatest:
[tex]\frac{3039}{1000}<\frac{3200}{1000}<\frac{3990}{1000}<\frac{8200}{1000}[/tex]
Now actual terms arranged from least to greatest will be:
[tex]3\frac{39}{1000}<3\frac{1}{5} <3\frac{99}{100}<3\frac{52}{10}[/tex]
Step-by-step explanation:
We need to arrange the weights [tex]3\frac{1}{5} ,3\frac{39}{1000},3\frac{99}{100},3\frac{52}{10}[/tex] from least to greatest.
To arrange them in least to greatest we need to convert them into improper fractions and then make their denominators same.
[tex]3\frac{1}{5}=\frac{16}{5} \\3\frac{39}{1000}=\frac{3039}{1000} \\3\frac{99}{100}=\frac{399}{100} \\3\frac{52}{10}=\frac{82}{10}[/tex]
Now, Making their denominator same by taking LCM of 5,1000,100 and 10
The LCM is 1000
Now the fractions will become:
[tex]\frac{16}{5}=\frac{16*200}{5*200}=\frac{3200}{1000}[/tex]
[tex]\frac{399}{100}=\frac{399*10}{100*10}=\frac{3990}{1000}[/tex]
[tex]\frac{82}{10}=\frac{82*100}{10*100}=\frac{8200}{1000}[/tex]
Now we have fractions: [tex]\frac{3200}{1000},\frac{3990}{1000},\frac{8200}{1000},\frac{3039}{1000}[/tex]
Now the smallest term will be one having smallest numerator
Arranging the terms from least to greatest:
[tex]\frac{3039}{1000}<\frac{3200}{1000}<\frac{3990}{1000}<\frac{8200}{1000}[/tex]
Now actual terms arranged from least to greatest will be:
[tex]3\frac{39}{1000}<3\frac{1}{5} <3\frac{99}{100}<3\frac{52}{10}[/tex]
Name the corresponding angle or side. a, b, c, or D
Answers
Answer:
I think it is B. LM
Step-by-step explanation:
i think this because the shape just looks like it is rotated.
777×900
Can u help me
Answers
1st Answer:
The answer to this would be 699,300!
Have a great day good luck! Plugging it into a calculator was easy^^
Answer:
699,300
Step-by-step explanation:
777x900=699,300
A map of a rectangular park has a length of 4 inches and a width of 6 inches. Ir uses a scale of 1 inch for every 10 miles. What is the area of the park? Is tthe answer 2,400 miles?
Answers
Answer:
yes, your answer would be 2400
Write the following as a base-10 numeral in standard form.
4 x 105 + 2 x 102 + 7 =
Answers
Answer:
631
Step-by-step explanation:
4x105=420
102*102=204
Rewrite the equation:
420+204+7= 631
Mikey bikes 12 miles in 2 hours. How many miles does Mikey bike in an hour?
Answers
Answer:
6 miles
Step-by-step explanation:
2 hours can be made into 1 hour by dividing by 2. In order to keep the ratio, you also have to divide the miles by 2, giving you 6.
2:12
1:6
Usa mmm para mostrar cada número.
Comienza con
este número.
Encierra en un
Escribe un
círculo es mayor
número para
que o es menor que comparar.
1.
es mayor que
es menor que
37
2.
es mayor que
es menor que
61
Answers
2. es menor que
The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of $29.81 per hour and a standard deviation of $9.31 per hour. What is the probability that the hourly pay of a randomly selected flight attendant:
a. Is between the mean and $35.00 per hour? (Round intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
b. Is more than $35.00 per hour? (Round intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
c. Is less than $20.00 per hour? (Round intermediate calculations to 2 decimal places and final answer to 4 decimal places.)
Answers
Answer:
a
[tex]P(29.81 < X < 35) = 0.21141[/tex]
b
[tex]P( X > 35) =0.28859[/tex]
c
[tex]P( X < 20) =0.14601[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = \$29.81[/tex]
The standard deviation is [tex]\sigma = \$9.31[/tex]
Generally the probability that the hourly pay of a randomly selected flight attendant Is between the mean and $35.00 per hour is mathematically represented as
[tex]P(29.81 < X < 35) = P( \frac{ 29.81 - 29.81 }{9.31} < \frac{x - \mu }{\sigma} < \frac{ 35 - 29.81 }{9.31} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(29.81 < X < 35) = P( 0 < Z < 0.5575 )[/tex]
=> [tex]P(29.81 < X < 35) = P( Z < 0.5575) - P( Z < 0)[/tex]
From the z table the area under the normal curve to the left corresponding to 0 and 0.5575 is
[tex]P( Z < 0) =0.5[/tex]
and
[tex]P( Z < 0.5575) = 0.71141[/tex]
=> [tex]P(29.81 < X < 35) = 0.71141 - 0.5[/tex]
=> [tex]P(29.81 < X < 35) = 0.21141[/tex]
Generally the probability that the hourly pay of a randomly selected flight attendant Is more than $35.00 per hour is mathematically represented as
[tex]P(X > 35) = P( \frac{x - \mu }{\sigma} > \frac{ 35 - 29.81 }{9.31} )[/tex]
[tex]P( X > 35) = P( Z > 0.5575 )[/tex]
From the z table the area under the normal curve to the right corresponding to 0.5575 is
[tex]P( Z > 0.5575 ) = 0.28859[/tex]
=> [tex]P( X > 35) =0.28859[/tex]
Generally the probability that the hourly pay of a randomly selected flight attendant Is less than $20.00 per hour is mathematically represented as
[tex]P(X <20 ) = P( \frac{x - \mu }{\sigma} < \frac{20 - 29.81 }{9.31} )[/tex]
[tex]P( X < 20) = P( Z < -1.0537 )[/tex]
From the z table the area under the normal curve to the right corresponding to -1.0537 is
[tex]P( Z < -1.0537 ) = 0.14601[/tex]
=> [tex]P( X < 20) =0.14601[/tex]
Brainliest if you provide a valid answer and explanation!
Q: Find the area!
Answers
Answer:
113.04 in^2
Step-by-step explanation:
A=pi*r^2
A=3.14*6^2
A=3.14*36
A=113.04
Answer
The area of the circle is [tex]36\pi[/tex] inches squared.
Explanation
The formula for the area of a circle is [tex]\pi r^{2}[/tex]. You are already given the radius (which is 6) so all you have to do is substitute the 6 for 'r' and solve the equation.
After substituting 6 for 'r' you get [tex]\pi 6^{2}[/tex].
According to PEMDAS, you have to solve 6 to the power of 2 first. 6 to the power of 2 is 36.
So the area of the circle is [tex]36\pi[/tex] inches squared.
If you would like to completely solve for the area, you can multiply 36 by 3.14. 36 times 3.14 equals 113.04. Note that this is not the exact answer, because [tex]\pi[/tex] is a never ending number, meaning if you multiplied both numbers, you product would also be a never ending number.
So the area of the circle is [tex]36\pi[/tex] or about [tex]113.04[/tex] inches squared.
WILL GIVE BRAINLIEST
Answers
what is (8+7 + 3.3) times ( 1/2) ^2
Answers
Answer & Step-by-step explanation: 4.58
PEMDAS:
Parenthesis first! (8 + 7 + 3.3) = 18.3
Exponents second! [tex]1/2^{2}[/tex] = 1/4 = 0.25
Multiply third and solve! 18.3 x 0.25 = 4.575
Round if needed! 4.575 = 4.58 = 4.6 = 5
Please help me I’m failing!!!
Answers
Write the decimal as a percent.
5.12
Answers
Answer:
512%
Step-by-step explanation:
5.12 × 100 = 512%, just multiply the decimal value by 100.
Answer:
512%
Step-by-step explanation:
take away the decimal point for it
walking in the winter wonderland here comes ________right down Santa claus lane
Answers
Answer:
Santa Claus
Step-by-step explanation:
It goes " walking in a winter wonderland here comes Santa Claus right down Santa Claus lane :) hope this helps
Answer:
Santa Clause
Step-by-step explanation:
Happy Holidays
Better Business Bureau conducted survey of 3,765 randomly selected residents of Laradise and found that 60% of them feel the businesses in Laradise, are run by compliant individuals. Find the best point estimate of the proportion of all residents of Laradise who believe businesses are run by compliant individuals.
a. In the prompt above what population parameter are you being asked about?
i. Proportion
ii. Mean
iii. Standard Deviation/Variance
iv. None of the above
b. What is the best point estimate?
c. What is the critical value (zα/2) or (tα/2) that corresponds to a confidence level of 99%?
d. Find the margin of error E, show the formula, fill in the pieces.
e. Construct the 99% confidence interval.
Answers
Answer:
a
i. Proportion
b
Best point estimate is [tex]\^ p = 0.60[/tex]
c
[tex]z_{\frac{\alpha }{2} } = 2.58 [/tex]
d
[tex]E = 0.0206 [/tex]
e
[tex] 0.5794 < p < 0.6206 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 3765
The proportion that feel the businesses in Laradise, are run by compliant individuals is [tex]\^ p = 0.60[/tex]
Considering question a
The correct option is Proportion because in the prompt we are told to obtain the fraction of the total sample size that has a particular attribute (which their opinion of business in Laradise) and this is what a proportion represents
Considering question b
The best point estimate is [tex]\^ p = 0.60[/tex] because this proportion best defines the fraction of the sample size who feel the businesses in Laradise, are run by compliant individuals
Considering question c
Generally given that the sample size is large enough n > 30 , it then means that the distribution is approximately normal so
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]z_{\frac{\alpha }{2} } = 2.58 [/tex]
Considering question d
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 2.58 * \sqrt{\frac{ 0.60 (1- 0.60 )}{ 3765} } [/tex]
=> [tex]E = 0.0206 [/tex]
Considering question e
Generally 99% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex] 0.60 -0.0206 < p < 0.60 + 0.0206[/tex]
=> [tex] 0.5794 < p < 0.6206 [/tex]
Whatcha ones are true and which are false
Answers
what's the question?
0.77 times 0.112 divided by 78 times 90
Answers
Answer:
0.0995076923
Step-by-step explanation:
(help!)
On a game show, Luke got to spin the wheel twice.
The first time, he got 900 points.
The second time, he got -200 points.
Assuming he started with no points, what was his total score?
A) 700
B) -700
C) 1100
D) - 1100
Answers
Answer:
a)700 is the answer that was easy