PLEASE HELP, ILL MARK BRAINLIEST
""solve triangle ABC using the given information round triangle measures to the nearest degree and side measure to the nearest tenth
Answers
9514 1404 393
Answer:
a) A = 73°, C = 59°, a = 16.7
b) A = 11°, C = 121°, a = 3.3
Step-by-step explanation:
The Law of Sines can be used to find angle C. Then the sum of angles in the triangle can be used to find angle A. The length of 'a' can be found either from the Law of Sines or the Law of Cosines at that point.
The given angle is opposite the shorter of the two given sides, so there are two possible solutions.
Acute triangle solution
The Law of Sines gives the relation ...
sin(C)/c = sin(B)/b
sin(C) = (c/b)sin(B)
C = arcsin(c/b·sin(B)) = arcsin(15/13·sin(48°)) ≈ 59°
Then angle A is 132° -59° = 73°, and side 'a' is ...
a = 13·sin(A)/sin(B) = 13·sin(73°)/sin(48°) ≈ 16.7
__
Obtuse triangle solution
The other value of arcsin(15/13·sin(48°)) is used:
C ≈ 121° ⇒ A = 11°
a = 13·sin(11°)/sin(48°) ≈ 3.3
__
The two solutions are ...
A = 73°, C = 59°, a = 16.7
A = 11°, C = 121°, a = 3.3
We note that the drawing is of an acute triangle, so that solution may be the one that is preferred.
_____
Additional comment
In the above presentation, we have rounded angle values to the precision required by the problem statement (nearest degree). However, in the actual calculations, we have used the full calculator precision. Only the final answers have been rounded.
Related Questions
20 points AND brainliest. Write an equation in slope intercept form to represent the table above. For example: y = 36x + 36. Please put enter a space after each term as shown in the example.
Answers
Answer:
This is a ratio table,so therefore there is always a pattern.
Step-by-step explanation:
In order to solve,you have to find the constant in the question,such as 30,40,50,and 60.The constant in this example is 10.When the constant is not even,or the numbers are not even,that's the time you pull out your notebook multiplication chart.Look at the numbers,and see if those numbers are on the chart.If all of them are on the chart,then see if one or both of the multiplicable numbers fall under the category of your variables.If all are under one number,then that number is your answer.
Together Mike and Sara ran 42 laps on the
track. Sara ran twice as many laps as
Mike did. Write a system of equations and
solve it to see how many laps they each ran.
Answers
Answer:
i dont know the system of equations since i only calculated it until i got the right answer but sara did 28 laps and mike did 14
happy april fools day you nerds now take my points
Answers
Answer:
WOW THANK YOU SO MUCH!
Step-by-step explanation:
I'm more of a dog lover and not a nerd, but hey I'll take what I can get!
If your like dogs, can you guess what kind of dog this is?
(yes they are all the same breed just different coat colors)
Select the correct answer.
Which of these is the standard form of the following function?
f(1) = 7(1 - 1)2 + 3
OA. f(x) = 7x2 14r + 10
OB. f(x)
7x2 14 - 10
O c. f(0) = -7x2 14r + 10
OD. f(x) = -732 – 141 – 10
Reset
Next
Answers
Answer:
answer is: 7x^2-14x+10
Step-by-step explanation:
4. Based on the original question, how many quarters and dimes must Jada have?
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URGENT: Find the value of X
Answers
Answer:
72x
Step-by-step explanation:
Plz, answer this question plz!
Answers
PLS HELPPP !! BRAINLIEST!!
Each cube in this figure is a 1/2 -centimeter cube. What is the total volume of the prism?
A. 4 1/2cm3
B. 1 1/2cm3
C. 6cm3
D. 18cm3
Answers
What is the value of n in the equation below?
StartFraction a Superscript n Over a cubed EndFraction = a Superscript 9
Answers
Answer:
ok ok it it 12
Step-by-step explanation:
stay safe 2021
Answer:
12
Step-by-step explanation:
Edge
Help, Help, Please
[tex] \sf find \: the \: value \: of \: \theta \: when \: \theta \: is \: acute\: angle[/tex]
[tex] \sf \cos^{2}(\theta) - \sin^{2}(\theta) =2-5 \cos(\theta) [/tex]
[tex]\text{note:explanation is a must}[/tex]
Answers
Answer:
θ = [tex]\frac{\pi }{3}[/tex] (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = [tex]\frac{1}{2}[/tex] , so
θ = [tex]cos^{-1}[/tex] ([tex]\frac{1}{2}[/tex] ) = [tex]\frac{\pi }{3}[/tex] ( or 60° )
Answer:
[tex] \huge \boxed{ \boxed{\blue{ { \theta = 60}^{ \circ} }}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:trigonometryPEMDASlet's solve:[tex] \sf \: rewrite \: \sin ^{2} ( \theta) \: as \: 1 - \cos ^{2} ( \theta) : \\ \sf \implies \: \cos ^{2} ( \theta) - (1 - \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: remove \: parentheses \: and \: change \: its \: sign : \\ \sf \implies \: \cos ^{2} ( \theta) - 1 + \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: add : \\ \sf \implies \: 2\cos ^{2} ( \theta) - 1 = 2 - 5 \cos( \theta) [/tex][tex] \sf \: move \: left \: hand \: sides \: expression \: to \: right \: hand \: sides \: : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 5 \cos( \theta) - 1 -2 = 0[/tex][tex] \sf \: rewrite \: 5\cos( \theta) \: as \: 6 \cos( \theta) - \cos( \theta) : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 6 \cos( \theta) - \cos( \theta) - 3 = 0[/tex][tex] \sf \:factor \: out \: 2 \cos( \theta) \: and \: - 1 : \\ \sf \implies \: 2\cos ( \theta)( \cos( \theta) + 3 ) -1( \cos( \theta) + 3) = 0[/tex][tex] \sf \: group: \\ \sf \implies \: (2\cos( \theta) - 1) ( \cos( \theta) + 3 ) = 0[/tex][tex] \sf \: rewrite \: as \: two \: seperate \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) - 1 = 0\\ \cos( \theta) + 3 = 0 \end{cases} [/tex][tex]\sf add \: 1 \: to \: the\: first \: equation \: and \: substract \: 3 \: from \: the \: second \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) = 1\\ \cos( \theta) = - 3 \end{cases} [/tex][tex] \sf the \: second \: eqution \: is \: false \: \\ \sf because \: - 1 \leqslant \cos( \theta) \leqslant 1 \: \\ \sf but \: we \: can \: still \: work \: with \: the \: second \: equation[/tex]
[tex] \sf substract \: both \: sides \: by \: 2 : \\ \implies\frac{ 2\cos( \theta) }{2} = \frac{1}{2} \\ \implies\cos( \theta) = \frac{1}{2} \\ \therefore \: \theta \: = {60}^{ \circ} [/tex]A coach is buying snacks for 22 players at a soccer match. She pays a total of $77 to buy each player a bottle of water and an energy bar. The price of one energy bar is $2. Which quantity is unknown? The price of a bottle of water. Let w equal the price of a bottle of water. Write an equation that represents the situation.
Answers
77*22= 1694 2*22=44
Step-by-step explanation:
22w + 44 = 77 is the equation which represents the situation and the price of a bottle of water is $1.5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let w be the price of a bottle of water.
The coach is buying 22 bottles of water and 22 energy bars, which cost a total of $77.
The cost of 22 energy bars is $2 x 22 = $44.
So the total cost of 22 bottles of water and 22 energy bars is:
22w + 44 = 77
We can simplify this equation by first subtracting 44 from both sides:
22w = 33
Then, we can solve for w by dividing both sides by 22:
w = 1.5
Therefore, 22w + 44 = 77 is the equation which represents the situation and the price of a bottle of water is $1.5.
To learn more on Equation:
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can someone help please
Answers
half of the triangle is a right angle triangle, so we use the phythagoras theorem and multipy our answer by 2
Carlos has 2.6 meters of wire. He has 3 projects for which he needs 0.9 meters each. Does carlos have enough wires?
Answers
Answer: Carlos does not have enough wires by 0.1 meters
Step-by-step explanation:
To determine if Carlos has enough wires, you need to find out the total amount of wires needed and then compare this to the amount of wires that Carlos has already.
= 0.9 + 0.9 + 0.9
= 2.7 meters
Carlos has 2.6 meters of wire but needs 2.7 meters.
Carlos therefore, does not have enough wires.
Please answer the question above.
Answers
Answer:
∠2 = 80°
Step-by-step explanation:
∠1 and ∠2 are supplementary angles (their sum is 180°)
1. What is the decimal equivalent of 3/
9? 0.2 0.3 0.4 0.5
Answers
Which expressions are equivalent to this exponential expression?
6-10
6-4
06-6
0 66
0
1
0
O
1
36
Answers
Answer:
6*6=36
Step-by-step explanation:
6*6. 6 with exponent of 2=36
3/5-the square root of 5
Answers
Answer:
1.341
Step-by-step explanation:
I'm smart at maths
QUESTION 6 / 10
Which of the following is not a source of income?
A. Your monthly student loan payment.
B. The stipend you receive for doing an internship.
C. Your annual salary for doing your job.
D. The wages you receive after a work shift.
Answers
Answer:
b. The stipend you receive.
Step-by-step explanation:
It would say paid intern if they were paid.
what is the sum of -4/7 and 6/7
Answers
Answer:
2/7
Step-by-step explanation:
Since the denominators are the same, we need to add the numerators and place it over the common denominator
-4+6 = 2
so
-4/7 + 6/7 = 2/7
2/7
Answer:
B
Step-by-step explanation:
License plates in the tiny country of Venn follow a unique pattern. The first character is one of 41 Egyptian hieroglyphs, the second is one of 39 emojis, and the third character is one of 10 polygons. How many 3 character license plates are available to the people of Venn?
Answers
Answer:
12710 license plates
Step-by-step explanation:
Given that :
First character = one of 41 different hieroglyphs
Second character = one of 31 emojis
Third character = one of 10 polygons
A license plate consists of 3 characters
Number of 3-character license plates available :
Number of hieroglyphs * Number of emojis * number of polygons
41 * 31 * 10 = 12710 license plates.
A survey was conducted on 800 students regarding the number of automobiles in their household. The population mean is 2.7 automobiles with a standard deviation of 0.7.
Which statement is true?
A.
There is a 95% certainty that the sample mean will fall within the interval 2.68 to 2.72.
B.
There is a 95% certainty that the sample mean will fall within the interval 2.67 to 2.73.
C.
There is a 95% certainty that the sample mean will fall within the interval 2.62 to 2.77.
D.
There is a 95% certainty that the sample mean will fall within the interval 2.65 to 2.75.
Answers
slope of 1/2 and y-intercept is -5.
Answers
Answer:
Y= 1/2x-5
Step-by-step explanation:
If a car has tires with a diameter of 28 inches and is traveling at 55 mph, how fast are its tires spinning, in rpm^ prime s (revolutions per minute)? [There are 63,360 inches in 1 mile) Round your final answer to 2 decimal places .
Answers
Answer:
The tires are spinning at 660.49 revolutions per minute.
Step-by-step explanation:
The speed of the tires (v) is the same that the speed of the car, so to find the angular velocity of the tires we need to use the equation:
[tex] \omega = \frac{v}{r} [/tex]
Where:
r: is the radius of the tires = d/2 = 28 inches/2 = 14 inches
[tex]\omega = \frac{55 mph}{14 inches*\frac{1 mile}{63360 inches}} = 2.49 \cdot 10^{5} \frac{rad}{h}*\frac{1 h}{60 min}*\frac{1 rev}{2\pi rad} = 660.49 rpm[/tex]
Therefore, the tires are spinning at 660.49 revolutions per minute.
I hope it helps you!
plz help me I only have 5 minutes left winner gets brainliest
In what year did the Apartheid Laws in South Africa end?
1990
1972
1994
1958
Answers
Answer:1994.
Step-by-step explanation:I need brainliest I helped with your other questions in comments pls
Find the apothem or height of the triangle. Round your answer at the end to the nearest tenth.
Answers
Answer:22.4
Step-by-step explanation:
Yea I'm bad at explaining
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Answers
Answer:
not sure but i think c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
What is the value of y in the equation below?
4y + 8 = 6y + 2
3/5
1
3
5
Answers
Answer:
y=3
Step-by-step explanation:
good luck
The base of a 14-foot ladder is 2 feet from a building. If the ladder reaches the flat roof , how tall is the building
Answers
a^2 + b^2 = c^2
14^2 + 2^2 = 200
squareroot 200 is abt 14.14
Answer:
Step-by-step explanation:
The height of the building is 8 rad 3
Approximately 13.9 ft
You buy a TV that costs $550 and you pay 6% sales tax. How much do you pay in total for the TV?
$33
$583
$517
$187
Answers
Answer:
$583 :)
Step-by-step explanation:
well we know the sales tax is %6 and to find out how much money it is equal to we have multiple $550 x 0.06. after that we get $33. Add $33 to $550 and you get $583!
Ab and cd intersects at e, aec=5x+12 and deb=8x-3
Answers
Answer:
x = 5
Step-by-step explanation:
Angles DEB and AEC are vertical angles, so they are congruent, and their measures are equal.
8x - 3 = 5x + 12
3x = 15