Solve the triangle. Round your answers to the nearest tenth.
Answers
Answer:
Angles: [tex]\angle A = 43^{\circ}[/tex] [tex]\angle B = 55^{\circ}[/tex] [tex]\angle C = 82^{\circ}[/tex]
Sides: [tex]BC = 20[/tex] [tex]AB = 29[/tex] [tex]AC =24[/tex]
Step-by-step explanation:
See attachment for complete question
From the attachment, we have:
[tex]AB = 29[/tex]
[tex]AC =24[/tex]
[tex]\angle C = 82^{\circ}[/tex]
Required
Complete the missing side and missing angles
To calculate angle B, we apply sine laws:
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
In this case:
[tex]\frac{AB}{sinC}=\frac{AC}{sinB}[/tex]
This gives:
[tex]\frac{29}{sin(82^{\circ})}=\frac{24}{sinB}[/tex]
[tex]\frac{29}{0.9903}=\frac{24}{sinB}[/tex]
Cross Multiply
[tex]sinB * 29 = 24 * 0.9903[/tex]
Divide both sides by 29
[tex]sinB = \frac{24 * 0.9903}{29}[/tex]
[tex]sinB = 0.8196[/tex]
Take arcsin of both sides
[tex]B = sin^{-1}(0.8196)[/tex]
[tex]B = 55^{\circ}[/tex]
So:
[tex]\angle B = 55^{\circ}[/tex]
To solve for the third angle, we make use of:
[tex]\angle A + \angle B + \angle C = 180^{\circ}[/tex]
This gives:
[tex]\angle A + 55^{\circ} + 82^{\circ} = 180^{\circ}[/tex]
[tex]\angle A + 137^{\circ}= 180^{\circ}[/tex]
[tex]\angle A = 180^{\circ}- 137^{\circ}[/tex]
[tex]\angle A = 43^{\circ}[/tex]
Hence, the angles are:
[tex]\angle A = 43^{\circ}[/tex] [tex]\angle B = 55^{\circ}[/tex] [tex]\angle C = 82^{\circ}[/tex]
To calculate the length of the third side, we apply cosine law
[tex]BC^2 = AB^2 + AC^2 - 2*AB*AC*cosA[/tex]
[tex]BC^2 = 29^2 + 24^2 - 2*29*24*cos(43^{\circ})[/tex]
[tex]BC^2 = 841+ 576 - 1392*cos(43^{\circ})[/tex]
[tex]BC^2 = 841+ 576 - 1392*0.7314[/tex]
[tex]BC^2 = 841+ 576 - 1018.11[/tex]
[tex]BC^2 = 398.89[/tex]
Take the square root of both sides
[tex]BC = \sqrt{398.89[/tex]
[tex]BC = 19.9722307217[/tex]
[tex]BC = 20[/tex]
Related Questions
please help
i’ll mark brainlyest
Answers
Answer:
x=7
Step-by-step explanation:
Generally accepted accounting principles reduce the problems associated with self-reported information. T/F?
Answers
Answer:
False
Step-by-step explanation:
Someone help me pls!
Answers
What is the estimated sum of 6/7+4/7
A.1/2
B.1
C.1 1/2
D.2
Answers
Answer:
1 1/2
Step-by-step explanation:
its 100% correct.
The lunch special at Omar's Restaurant is a sandwich, a drink and a dessert. There are 2 sandwiches, 2 drinks, and 2 desserts to choose from. How many lunch specials are possible?
Answers
Answer:
The number of lunch specials possible is 8.
Step-by-step explanation:
• If there are 2 sandwiches, 2 drinks, and 2 desserts to choose from and the lunch special is a sandwich, drink, and dessert:
• To find out the answer, we are going to say that we have sandwich a & sandwich b, drink a & drink b, and dessert a & dessert b:
1.) Sandwich a:
drink adessert a2.) Sandwich a:
drink adessert3.) Sandwich a:
drink bdessert b4.) Sandwich a:
drink bdessert a5.) Sandwich b:
drink adessert a6.) Sandwich b:
drink a dessert b7.) Sandwich b:
drink bdessert b8.) Sandwich b:
drink bdessert aPlease mark me the Brainliest!?!
The number of lunch specials possible is 8.
What is the combination in maths?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
If there are 2 sandwiches, 2 drinks, and 2 desserts to choose from and the lunch special is a sandwich, drink, and dessert.
The total choices are 3 in that 2 options for every choice are available.
Thus total combination can be made = 2³
total combination can be made = 8
Therefore, the total number of possible lunch specials is 8.
Learn more about combination here:
https://brainly.com/question/13474651
#SPJ2
If antique piece is sold for $1200 at gain of 30 % on sale price then the profit is
Answers
A classmate ordered these numbers from greatest to least. is she correct? construct an argument to justify your answer. 6.85, 6.58, - 6.8, - 6.5
Answers
Answer:
She is incorrect.
Step-by-step explanation:
-6.8 is less than -6.5 as they are negative numbers.
A recipe for trail mix uses 7 ounces of almonds with 5 ounces of raisins. (Almonds and raisins are the only ingredients.)
1. How many ounces of almonds would be in a one-pound bag of this trail mix?
2. Explain or show your reasoning. (OPTIONAL)
Answers
Answer:
Step-by-step explanation:
when you combine the amount of almonds and raisins, you get 12 ounces. so out of those 12 ounces, 7 is going to be almonds. aka [tex]\frac{7}{12}[/tex]. now you just have to multiply that by 16 (since there are 16 ounces in a pound) and you'll get roughly 9.333
Why are 9th Graders still working on Fractions/Decimals/Percentages?
Answers
Answer:
Rigged
Step-by-step explanation:
The 9th grade system is rigged.
Stefan sells Jin a bicycle for $103 and a helmet for $18. The total cost for Jin is 110% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answers
Answer:
$110
Step-by-step explanation:
If 110% = $103 + $18
110% = $ 121
Then 100% = ?
(100 ÷ 110) × 121 = $110
Amount Stefan spent = $103 + 18
= $121
Amount Jin made = $121 - 110
= $11
A popular candy is manufactured to weigh 0.16 ounces per piece. The pieces aresold in packages of 36. If the allowable amount of variation in weight for onepiece of candy is 0.03 ounces, which of the following equations can be used todetermine the highest and lowest allowable weight, w, of a package of 36 pieces?Assume that the weight of the packaging is negligible
a. â£wâ0.16â£/36=0.03
b. â£wâ5.76â£/36=0.03
c. 36 |wâ0.16| =0.03
d. 36|w-5.76|=0.03
Answers
Answer:
B.) |w - 5.76| / 36 = 0.03
Step-by-step explanation:
Given :
Weight of individual candy piece = 0.16 ounce
Number of candy pieces per package = 36
Allowable variation in weight of individual piece = 0.03 ounces
The highest and lowest allowable weight, w of a package of 36 pieces ;
Actual manufacturing weight of entire 36 candy = (36 * 0.16) = 5.76
Allowable weight ± actual weight ≤ allowable variation
w ± 0.16 ≤ 0.03
|w - 0.16| ≤ 0.03
For the entire 36 candy pieces :
|w - 0.16*36| = 0.03 * 36
|w - 5.76| = 1.08
|w - 0.16*36| = 0.03 * 36
Could also be written as :
|w - 5.76| / 36 = 0.03
agbdsgbdsbdsbdgbsdagbdsgbdsbdsbdgbsd
Answers
Answer:
holy that sucks for you like wow
Answer:
WHAT IS THAT
Step-by-step explanation:
IT LOOKS LIKE THIS :
HSIOALXVBHSOQPSBSHIAOSKXX
Write the ordered pairs when rotated 90 clockwise around the origin A (2,-3) B (-4,6) C (-5, -7)
Answers
Myles is working on his typing. He types for 3 minutes straight and is able to type 150 words. Determine how long it would take for Myles to type 900 words.
Answers
HELLLLLP ESGESGKSEGKESKGKSEKGESKKKS KKSGEKSGKSKEK GKSEGKKSEGKK what is 1+!
Answers
If it takes a secretary 20 which type 400 pages how many pages can he
type in 45 minutes
Answers
Answer:
I think its 20 minutes
am i right?
Step-by-step explanation:
I am not sure about my ans
but..
it can 800 or more pages
hope it helps you...
Answer:
900pages=45minutes
Step-by-step explanation:
Step 1: Find the unit rate=how many pages he can type in 1 minute
to find the unit rate,
k=y/x
y=400 pages
x=20 min
400/20=20 pages in 1 minute
Step 2: Multiply the amount of pages by 45
k times x = y
20 times 45= 900 pages in 45 minutes
So, it will take the secretary 45 minutes to type 900 pages.
Determine x in the figure.
74°
2xº
Answers
Answer:
-37
Step-by-step explanation:
Simplifying
74 + 2x = 0
Solving
74 + 2x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-74' to each side of the equation.
74 + -74 + 2x = 0 + -74
Combine like terms: 74 + -74 = 0
0 + 2x = 0 + -74
2x = 0 + -74
Combine like terms: 0 + -74 = -74
2x = -74
Divide each side by '2'.
x = -37
Simplifying
x = -37
There are 4 veggie pizzas for every 5 cheese pizzas. How many cheese pizzas are there if 108 pizzas total are ordered? please show work
Answers
Answer:
6.25
Step-by-step explanation:
Answer:
60 because [total of pizzas]/(veggie + cheese)= 12 ((108/(4+5) = 12)) so you take 5 (the amount of cheese pizzas) and multiply it by 12 to get 60
sorry if i explained it bad im not too good at explaining
Help I need this done ASAP
Answers
Answer:
im taking s nap
Step-by-step explanation:
I would like some real-world situations that use linear input-output relationship, however, it must be unique. Not simple examples such as a vending machine, but something that's more unique (make sure it's linear).
Answers
Answer:
given a linear function represented by a table of values and a linear function ... Students may have trouble with the word unique. ... How do you determine if relations are functions? ... How can you use functions to model real-world situations? ... said while there was input and output, she thought the machine was more like a.
Step-by-step explanation:
A military cannon is placed at the base of a hill. The cannon is fired at an angle toward the hill. The path
of the cannon ball is parabolic and can be represented by y = -0.05x^2 + 5x + 1, where y represents
the height of the ball in meters and x represents the horizontal distance of the ball from the cannon
The incline of the hill can be represented by the equation y = 0.725x. How far will the cannon ball have
moved horizontal from the cannon when it hits the hill?
Answers
Answer:
Algebracicaly speaking the answer would be either -13.3876 or - 158.612 through the quadratic equation, but these answers don’t make sense in this real world scenario.
Step-by-step explanation:
Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = x2 + 9 Shift the graph of y = x2 left 9 units. Shift the graph of y = x2 right 9 units. Shift the graph of y = x2 down 9 units. Shift the graph of y = x2 up 9 units.
Answers
Answer:
Shift of graph of y=x^2 up 9 units.
Option D is correct option.
Step-by-step explanation:
We are given:
[tex]y = x^2[/tex]
We need to describe how the graph of [tex]y = x^2[/tex] can be transformed to the graph of the given equation [tex]y=x^2+9[/tex]
We know the transformation rule:
If f(x) is transformed into f(x)+h, the graph is transformed vertically up h units.
So, In our case:
[tex]y=x^2[/tex] is transformed into [tex]y=x^2+9[/tex]
So, The graph is transformed vertically up 9 units.
Or we can write, shift of graph of y=x^2 up 9 units.
Option D is correct option.
a six sided die is rolled once what is the probability of rolling the die and landing on number 5 first and then rolling it again and landing on 3? pls help
Answers
Answer:
i got into B or C
Step-by-step explanation:
3x-5y=2 slope intercept
Answers
Answer:
x = (2+5y)/3y = (-2+3x)/5Step-by-step explanation:
3x - 5y = 2
3x = 2+5y
x = (2+5y)/3
-5y = 2-3x
5y = -2+3x
y = (-2+3x)/5
HOPE THIS HELPS YOU
Which expression is equivalent to 7(4+7)? *
Answers
Answer:
28+49
Step-by-step explanation:
1. Find the missing measure.
Answers
90-65= 25
Pls help urgently extra points and mark brainlist
Answers
Answer: 5 is your answer
Step-by-step explanation:
Please help, I will give brainliest. I am struggling badly.
Answers
Answer:
(C) y = x/2 + 2
Divide 12.33 by 9 and write the quotient. (Show steps of working
Answers
9514 1404 393
Answer:
1.37; see attached
Step-by-step explanation:
The steps of long division are shown in the first attachment.
My favorite way to do arithmetic of this sort is shown in the second attachment. (That is, use a calculator.)
Whoever can answer these 4 will get branliest, thanks! :)
Answers
Answer:1 : 22.5
2 : 20 games
3 : 575
4 : Grant can purchase 7 base ball cards packs in $21
Step-by-step explanation: OK first divide 90 by 4 to see how many words per minute
1# 90 ÷ 4 = 22.5
OK, then multiply 22.5 by 10 for your answer
Your answer is;
225 words per 10 minutes
2#Hope I Helped!!! 7*4=28 and 5*4=20 so about 20 games.
3# 2p=230
divide 2
Each slice of pizza is 115 calories.
5p=c
5(115)=c
575= Calories
Grant paid $12 for 4 baseball card packs.
So, in $1 he will purchase, cards
And in $21, he will purchase = 7
Therefore, Grant can purchase 7 base ball cards packs in $21.