Solve the triangle, find m∠A and m∠C. Round angles to the nearest degree.
m∠A= __∘
m∠C= __∘
Answers
Answer:
[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of the triangle is called the hypotenuse and the other two sides are called the legs.
Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.
The cosine ratio is defined as:
[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
Note the angle A of the figure has 17 as the adjacent leg and 38 as the hypotenuse, so we can directly apply the formula:
[tex]\displaystyle \cos A=\frac{17}{38}[/tex]
[tex]\cos A=0.4474[/tex]
Using a scientific calculator, we get the inverse cosine:
[tex]A=\arccos(0.4474)[/tex]
[tex]A\approx 63^\circ[/tex]
Since A+B+C=180°, we can solve for C:
C = 180° - A - B
C = 180° - 63° - 90°
C = 26°
Thus:
[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]
In the given right triangle ABC, m∠A ≈ 26.44° and m∠C ≈ 63.56°.
To solve the right triangle ABC, we can use trigonometric ratios. In a right triangle, the three main trigonometric ratios are:
1. Sine (sin): [tex]\(\sin(\theta) = \frac{{\text{opposite side}}}{{\text{hypotenuse}}}\)[/tex]
2. Cosine (cos): [tex]\(\cos(\theta) = \frac{{\text{adjacent side}}}{{\text{hypotenuse}}}\)[/tex]
3. Tangent (tan): [tex]\(\tan(\theta) = \frac{{\text{opposite side}}}{{\text{adjacent side}}}\)[/tex]
Given:
AC = 38
AB = 17
To find the angles m∠A and m∠C, we can use the sine and cosine ratios, respectively.
1. For m∠A:
[tex]\(\sin(m\angle A) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle A= \sin^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]
2. For m∠C:
[tex]\(\cos(m\angle C) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle C = \cos^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]
Let's calculate the angles:
[tex]1. \(m\angle A \approx \sin^{-1}\left(\frac{{17}}{{38}}\right) \approx 26.44^\circ\)\\\\2. \(m\angle C \approx \cos^{-1}\left(\frac{{17}}{{38}}\right) \approx 63.56^\circ\)[/tex]
Therefore, m∠A ≈ 26.44° and m∠C ≈ 63.56° (rounded to the nearest degree).
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Related Questions
Which of the following is an equivalent expression to the given expression using the commutative property of addition?
2(xy)+5x
Question 1 options:
(xy)2+5x
(2x)y+5x
5x+2(xy)
x(2y+5)
Answers
Answer:
I think it's the 2rd equation
0.571428
is or is not the decimal equivalent of
4
7
. Write your answer in the space provided.
Answers
Answer:
4 ÷ 7 = 0.571428
Step-by-step explanation:
4 ÷ 7 = 0.571428
Lickety Sweet's Candy Store sells candy by the ounce. Maura paid $3.48 for a 12-ounce bag of hard watermelon candies and $1.28 for an 8-ounce bag of chewy chocolate candies. How much more do the watermelon candies cost per ounce than the chocolate candies?
Answers
Answer:
The Watermelon candies cost 13 more cents then the chocolate.
Step-by-step explanation:
$3.48 divided by 12 is 29 cents
$1.28 divided by 8 is 16 cents
Subtract 16 from 29 and get 13
If Lickety Sweet's Candy Store sells candy by the ounce. Maura paid $3.48 for a 12-ounce bag of hard watermelon candies and $1.28 for an 8-ounce bag of chewy chocolate candies, then she paid 13 more cents for watermelon candies cost per ounce than the chocolate candies
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Lickety Sweet's Candy Store sells candy by the ounce.
For 12-ounce bag of hard watermelon candies Maura paid $3.48
For 8-ounce bag of chewy chocolate candies Maura paid $1.28
Let us find cost of each watermelon candie
$3.48 divided by 12
3.48/12=29 cents
$1.28 divided by 8
1.28/8=16 cents
Subtract 16 from 29 and get 13
29-16=13
Hence 13 cents more do the watermelon candies cost per ounce than the chocolate candies
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30 POINTS What is the answer????
Answers
Answer:
Step-by-step explanation:
the third i think
I’ll post part one but plz help it’s worth 15POINTS I’ll mark as Well!!!!
Answers
Answer:
Wellll
Step-by-step explanation:
what is speed of sound in air at 100 degree celcius?
Answers
Answer:
386m/s is the answer to your question
Triangle has side lengths 2, 3, and 4.
Triangle has side lengths 4, 5, and 6.
Is Triangle similar to Triangle?
Answers
Answer:
I think no
Step-by-step explanation:
I would say no because they would all have to be the same. 2/4= 1/2 so all the side lengths would have to divide into one half, and they don't
A scratch-off lottery ticket has 14 concealed spaces among which are 4 symbols saying "Win!". The person who bought the ticket scratches the black yucky stuff off 3 spaces, winning an instant $10 if all three are winners. What's the probability of winning this game? I'm confused about this please help!
Answers
Answer:
Step-by-step explanation:
since this has something to do with chance im guessing maybe percentage of winnign this
so
4/14 x 100 so 28.57% probability of winning this game i believe
Exact answer as a fraction = 1/91
Approximate answer in decimal form = 0.010989
Approximate answer in percent form = 1.0989%
=====================================================
Explanation:
Let's think of the problem another way.
Let's say that we have 14 ping pong balls labeled 1 through 14. Furthermore, lets set up the first four balls {1,2,3,4} to be labeled with a star sticker. The rest don't have a star. The star stickers indicate a winning ball. All of the ping pong balls are then put into a bag where we will randomly pull out 3 of them. Replacements will not be made (ie the ball won't be put back). The goal is to get 3 star stickers in a row.
One possible combination is {1,2,7} which is close but not a winner since that 7 is there. Another possible combination is {5,8,12} which is not even close to a winner (since we didn't get 1,2,3 or 4).
---------
We have two questions we need to answer:
How many possible combinations are there? How many combinations are a winner?We'll use the nCr combination formula
[tex]_nC_r = \frac{n!}{r!*(n-r)!}[/tex]
We use the combination formula, instead of the permutation formula, because order does not matter. Something like {1,2,7} is the same as {7,1,2}.
If you plug in n = 14 and r = 3, you should find that 14 C 3 = 364.
I'll list the steps in the attached image below (to save space here).
This means there are 364 different ways to play the game. In other words, there are 364 ways to pull out three ping pong balls.
---------
That wraps up question 1. Now onto question 2.
We have 4 winning balls and 3 slots to fill, so we will plug n = 4 and r = 3 into the combination formula. I'll skip the steps because they're fairly similar to earlier. You could also use Pascal's Triangle to help. Whichever method you use, you should find that 4 C 3 = 4.
note: we have 4 winning balls and 3 slots to fill, so you can think of it like "how many ways are there to not choose a ball?" and that answer would be 4.
So this means there are 4 ways to win the game.
------------------------------------
In summary so far, we found
There are 364 ways to play the gameThere are 4 ways to win the gameThis means the probability of winning is 4/364 = 1/91
Use your calculator to find that 1/91 = 0.010989 approximately which converts over to the approximate percentage of 1.0989%
In the ordered pair (2, 3), 3 is the
Answers
Pretty sure that’s right
Help I mark brainliest
Answers
Answer:
-r ^3
Step-by-step explanation:
fatore a equação
2x²-3xy-2y²-2x-11y-12
Answers
2x²-3xy-2y²-2x-11y-12
Write -3xy as a difference
2x²+xy-4xy-2y²-2x-11y-12
write -2x as a difference
2x²+xy-4xy-2y²+4x-6x-11y-12
Write -11y as a difference
2x²+xy-4xy-2y²+4x-6x-8y-3y-12
Factor out 2x from the expression
2x×(x-2y-3)+xy-2y²+4x-8y-3y-12
Factor out y from the expression
2x×(x-2y-3)+y×(x-2y-3)+4x-8y-12
Factor out 4 from the expression
2x×(x-2y-3)+y×(x-2y-3)+4(x-2y-3)
Factor out x-2y-3 from the expression
Answer: (x-2y-3)x(2x+y+4)
PLEASE MARK ME AS BRAINLIEST!!
What is the solution to
{y=14x+3y=2x+10
Answers
Answer:
The solution is ([tex]\frac{7}{12}[/tex] , [tex]\frac{67}{6}[/tex])
Step-by-step explanation:
∵ y = 14x + 3 ⇒ (1)
∵ y = 2x + 10 ⇒ (2)
→ Equate equations (1) and (2) to find x
∵ 14x + 3 = 2x + 10
→ Subtract 2x from both sides
∴ 14x - 2x + 3 = 2x - 2x + 10
∴ 12x + 3 = 10
→ Subtract 3 from both sides
∴ 12x + 3 - 3 = 10 - 3
∴ 12x = 7
→ Divide both sides by 12 to find x
∵ [tex]\frac{12x}{12}[/tex] [tex]\frac{7}{12}[/tex]
∴ x = [tex]\frac{7}{12}[/tex]
→ Substitute the value of x in equation (1) or (2) to find y
∵ y = 2([tex]\frac{7}{12}[/tex]) + 10
∴ y = [tex]\frac{7}{6}[/tex] + 10
∴ y = [tex]\frac{67}{6}[/tex]
∴ The solution is ([tex]\frac{7}{12}[/tex] , [tex]\frac{67}{6}[/tex])
)A triangle is shown on the graph:
What effect will a 90-degree clockwise rotation have on the triangle? Be sure to address how it could impact the angles, side lengths, and any congruency between the original pre-image and the image.
Answers
Answer:
45
Step-by-step explanation:
Answer:
45 idrk
Step-by-step explanation:
SCOOBY-dooby-do-la-de-da-de-da
what is the answer?
Answers
a triangle equals 180 degrees, 2 angles are given 47 degrees and the 90 degree angle that makes a right square. 90+47=137. 180-37=43.
Which of the following is the missing value?
a. 0.27
b. 0.30
c. 0.37
d. 0.50
Answers
Answer:
answer is b
Step-by-step explanation:
Please answer correctly !!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!
Answers
Answer:
That looks like interior angle to me
x = 47 (since interior angles are congruent)
Step-by-step explanation:
I am really sleepy... :/
Is a quadrilateral a square?
Answers
Answer:
No but a square is a quadrilateral
Step-by-step explanation:
hope this helps :)
Answer:
If I were to be honest no Edit: yes it is
Step-by-step explanation:
No because a square has straight parrallel corners. But a quadrilateral has slanted parallel corners.
Hope that helped. But maybe wait for sumone else to answer too. : )
Edit: nvm my bad I was wrong
Write 24/25 as a decimal.
Answers
write as an algebraic expression: Two less than two times a number (y).
Answers
Answer: 2y-2
Step-by-step explanation:
Y represents the number
If you were to solve this you would have to do 2 times a number which is shown by 2y.
Then, you need to subtract 2 from 2y.
Therefore, the answer is 2y-2
The expression for the given verbal expression is 2y-2.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is a verbal expression, Two less than two times a number.
We need to convert it into mathematical expression,
Let the number be y,
Therefore, two times a number = 2y
And Two less than = -2
Therefore,
Two less than two times a number = 2y-2
Hence, the expression for the given verbal expression is 2y-2.
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Can someone please answer these questions???!
Answers
Answer:
Step-by-step explanation:
sub in all your x values into the linear equation it gives you
once you have your table you should be able to figure out the rest if the questions !!
which of the following quadrilaterals are always parallelogram? select all that apply
Answers
Answer: square, rectangle and rhombus
Step-by-step explanation:
Two containers P and Q are filled with different amounts of water. Each container has a small hole. The graph shows the amount of water, V milliliters, left in each container after x minutes.
Explain what the y-intercept means in this scenario.
Answers
Answer:
Step-by-step explanation:
Equation of the line for container O and container P will be in the form of,
y = mx + b
Here m = slope of the line = Change in amount of water per minute
b = y-intercept
From the graph attached,
y-intercept 'b' represents the initial amount of water in the container.
For container O, initial amount of water in the container is 1000 mL.
Similarly, initial amount in the container is 900 mL.
Colton bounces a ball 3.268 feet infront of his feet. The path of the ball from the time it hits the ground until it lands on the floor is represented by
Answers
here is the complete and correct question. Colton bounces a ball 3.268 feet in front of his feet. The path of
the ball from the time it hits the ground until it lands on the floor is represented by
f(x) =-4(x - 5)2 + 12
Assuming that Colton's feet are located at the origin, (0, 0), what is the maximum height of the ball (in feet)?
Answer:
12ft
step by step explanation:
This equation has been written in vertex form, and it has its vertex at (5, 12). Because the scale factor is not positive, it has a negative value, the graph for the question is going to open downward, such that the vertex,
that is the maximum height is 12 ft.
we have The equation of a parabola with vertex (h, k) to be
f(x) = a(x -h)² + k
when put in Comparison to your question function, we get that
a=-4
h=5
k=12
so the vertex (h, k) = (5, 12).
Estimate to the nearest integer.
21
O 3
O 4
O 5
Answers
Answer:
5
Step-by-step explanation:
So the square root of 21 is 4.582...
If you round 4.582.. it is 5
Because you look at the first number behind the decimal (tenths place) if it is 4-0 you leave the number the same. If it is 5-9 you increase the number by 1.
Hope this helps ya!!
Find the value of each variable
Answers
Answer:
Step-by-step explanation:
[tex]\sqrt{c^2 + c^2 }[/tex] = 9√2
c√2 = 9√2 ⇒ c = 9
b = 2c ⇒ b = 18
d = [tex]\sqrt{18^2 - 9^2 }[/tex] = [tex]\sqrt{(18 - 9)(18+9)}[/tex] = √243 = 9√3
a = c = 9
b = 18
d = 9√3
Suppose your community has 3580 people this year. The population is growing 2.5% each year. a. Write an exponential function to model the population. b. What will the population be in 3 years? c. Graph the function and give the domain and range.
Answers
Answer:
Step-by-step explanation
sadly i dont understand
if y = 4 when x = -4 find y when x = 7
Answers
Answer:
-7
Step-by-step explanation:
Assuming y and x are the opposites of each other, when x = 7 y must be -7.
Which values represent solutions to the equation?
Tan(3Pi/4-2x)=-1, where x = [0,pi]
Answers
The value of the variable x will be {0, pi/2, pi}. Then the correct option is B.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The trigonometric equation is given below.
tan (3π/4 - 2x) = - 1
We know that the value of tan 3π / 3 is negative one. Then the equation will be
tan (3π/4 - 2x) = tan 3π/4
Apply inverse of tangent on both sides, then the equation will be
(3π/4 - 2x) = 3π/4, -π / 4
- 2x = 0, -π
2x = 0, π
x = 0, π/2
Then the value of the variable x will be {0, pi/2, pi}.
Then the correct option is B.
The question was incomplete, but the complete question is given below.
Which values represent solutions to the equation? tan(3pi/4 - 2x) = -1, where x ∈ [0,pi]
A) {0, pi}
B) {0, pi/2, pi}
C) {0, pi, 2pi}
D) {0, pi/2, pi ⋅ 3pi/2}
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lemon made 8 5/8 cups of lemonade. she drank 4 3/8 cups of the lemonade. how many cups of lemonade does she have left
Answers
Answer: 4 1/4
Step-by-step explanation:
8 5/8
-4 3/8
4 2/8 or 4 1/4
Solve |x| < 12
I’m so lost with this stuff.
Answers
Answer: (-12,12)
Step-by-step explanation: hope it helps!