Which trigonometric ratios are correct for triangle
ABC? Select three options.

Which Trigonometric Ratios Are Correct For TriangleABC? Select Three Options.

Answers

Answer 1

Answer:

Options (1), (3) and (4)

Step-by-step explanation:

From ΔABC given in the picture,

By Pythagoras theorem

Hypotenuse² = (Leg 1)² + (Leg 2)²

BC² = AB² + AC²

(18)² = 9² + AC²

AC = [tex]\sqrt{324-81}[/tex]

AC = [tex]9\sqrt{3}[/tex] cm  

sin(C) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

         = [tex]\frac{AB}{BC}[/tex]

         = [tex]\frac{9\sqrt{3}}{18}[/tex]

sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex]

sin(B) = [tex]\frac{AC}{BC}[/tex]

         = [tex]\frac{9}{18}[/tex]

         = [tex]\frac{1}{2}[/tex]

cos(B) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

          = [tex]\frac{9\sqrt{3}}{18}[/tex]

          = [tex]\frac{\sqrt{3} }{2}[/tex]

tan(B) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

          = [tex]\frac{AC}{AB}[/tex]

          = [tex]\frac{9}{9\sqrt{3} }[/tex]

          = [tex]\frac{1}{\sqrt{3} }[/tex]

tan(C) = [tex]\frac{AB}{AC}[/tex]

          = [tex]\frac{9\sqrt{3}}{9}[/tex]

          = [tex]\sqrt{3}[/tex]

Therefore, Options (1), (3) and (4) are the correct options.

Answer 2

Answer:

Options (1), (3) and (4)

Step-by-step explanation:

From ΔABC given in the picture,

By Pythagoras theorem

Hypotenuse² = (Leg 1)² + (Leg 2)²

BC² = AB² + AC²

(18)² = 9² + AC²

AC =

AC =  cm  

sin(C) =

        =

        =

sin(C) =

sin(B) =

        =

        =

cos(B) =

         =

         =

tan(B) =

         =

         =

         =

tan(C) =

         =

         =

Therefore, Options (1), (3) and (4) are the correct options.Step-by-step explanation:


Related Questions

Pls help it's due tonight!!!
:((((((

Answers

i think AB is 3!!

i hope i’m right good luck ,:D

Answer:

∆EDA~∆ECB (AAA)

3÷ (15+3) = AB ÷ (12+AB)

AB = 2.4

Which three dimensional figures could be used

Answers

Answer:

A cube, rectangular prism, sphere, cone and cylinder are the basic 3-dimensional shapes we see around us.

62
.
52
=
27
.
39
+
t

Answers

Answer:

t = 35.13

Step-by-step explanation:

Simplifying

62.52 = 27.39 + t

Solving

62.52 = 27.39 + t

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-1t' to each side of the equation.

62.52 + -1t = 27.39 + t + -1t

Combine like terms: t + -1t = 0

62.52 + -1t = 27.39 + 0

62.52 + -1t = 27.39

Add '-62.52' to each side of the equation.

62.52 + -62.52 + -1t = 27.39 + -62.52

Combine like terms: 62.52 + -62.52 = 0.00

0.00 + -1t = 27.39 + -62.52

-1t = 27.39 + -62.52

Combine like terms: 27.39 + -62.52 = -35.13

-1t = -35.13

Divide each side by '-1'.

t = 35.13

Simplifying

t = 35.13

hope it helps !!!!!!!!!!!    :)

5x^2-4x=6 help!!! Thank you in advance !

Answers

the answer is c ahaha you’re welcome

Answer:

x = 2 ± √34/5

Step-by-step explanation:

Move terms to the left side.

5x^2 - 4x = 6

5x^2 - 4x -6 = 0

Identify a, b, and c before plugging them into the quadratic formula.

a = 5

b = -4

c = -6

x = -(-4) ± √(-4)^2 - 4 * 5(-6)/2 * 5

Then simplify.

Please Help! One natural number is 4 more than the other one. The product of the two numbers is three times the square of the smaller number. Find the numbers.​

Answers

Let n and n+4 be the numbers. Then:

n² + 3(n+4)=66

n²+3n-54=0

(n+9)(n-6)=0

n=6 or -9

n+4=10

Assuming positive integers only, the numbers are 6 and 10…..

Step-by-step explanation:

100% right

Answer:

2 and 6

Step-by-step explanation:

Many studies have investigated the question of whether people tend to think of an odd or an even number when they are asked to think of a single-digit number (0 through 9). Combining results from several studies, Kubovy and Psotka (1976) used a sample of 1,770 people, of whom 741 thought of an even number and 1,029 thought of an odd number. Would a one-sided or a two-sided alternative hypothesis be more appropriate in this case

Answers

Answer:

A two-sided alternative hypothesis would be more appropriate in this case

Step-by-step explanation:

A one-sided hypothesis is one that asserts that a given parameter is either smaller than the null hypothesis value or larger than the value presented by the null hypothesis.

However in a two sided hypothesis, the claim is made that a given parameter is not equal to the parameter given in the null hypothesis, such that the parameter can be either larger than than or lesser than the value of the null hypothesis and still satisfy the condition of the hypothesis

Therefore, given for that for there to be a conclusion, the test should be weather the number of people that think of an odd number are equal to the number of people that think of an even number, or weather the number of people that think of an odd number are not equal to the number of people that think of an even number

Therefore, a two-sided hypothesis should be used since the claim (that the numbers are not equal) is not equal to the value of the parameter in the null hypothesis (that the numbers are equal)

PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!

Answers

relative dating is the answer

A roll of quarters has a value of
$10. The expression
10 represents the amount of money in a number of rolls of quarters. What does the variable

represent?

Answers

Answer:

110

Step-by-step explanation:

16 and 3/5 - 4 and 4/5 equals

Answers

The answer is 11 4/5

Answer:

59/5

Step-by-step explanation:

16 and 3/5 = 83/5

4 and 4/5 = 24/5

83/5 - 24/5 = 59/5

Simplify the following expression:
(i-3) +6i-3(8 - i)
A. 21+7
B. -27 +10;
C. 14 +6;
D. 8 +41

Answers

The complex expression (i-3) +6i-3(8 - i) when simplified is -27 + 10i

How to simplify the complex expression

From the question, we have the following parameters that can be used in our computation:

(i-3) +6i-3(8 - i)

Express properly

So, we have

(i - 3) + 6i - 3(8 - i)

When the brackets are opened, we have

(i - 3) + 6i - 3(8 - i) = i - 3 + 6i - 24 + 3i

Collect the like terms

So, we have

(i - 3) + 6i - 3(8 - i) = - 3  - 24 + i + 6i + 3i

Evaluate the like terms

So, we have

(i - 3) + 6i - 3(8 - i) = -27 + 10i

Hence, the complex expression when simplified is -27 + 10i

Read more about expression at

https://brainly.com/question/28792378

#SPJ1

Data represented by quantities is called data.

Answers

Four types of data (nominal, ordinal, interval, and ratio) that represent values or observations that can be sorted into a category

Solve the solution of this inequality
9−4d≥−3

Answers

Answer: d

3

Step-by-step explanation: that’s the answer buddy

Answer: X is less than or equal to 3.

I am 100% sure it's right.

Step-by-step explanation:

A guy wire supporting a radio tower is positioned 145 feet up the tower.
It forms a 45°angle with the ground.
About how long is the wire? Round your answer to the nearest whole
number.

Answers

the angle of the tower would be the coifficent

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y2=x,x=2yy 2 =x,x=2y; about the y-axis

Answers

Answer:

Step-by-step explanation:

From the first image attached below, we will see the sketch of the curve x = y² & x = 2y

In the picture connected underneath, the concealed locale(shaded region) is bounded by the given curves. Now, we discover the marks of the crossing point of the curves. These curves will cross, when:

[tex]y^2 =2 y \\ \\ or y^2 -2y = 0 \\ \\ y(y-2) = 0 \\ \\ y = 0 \ \ or \ \ y = 2[/tex]

Thus, the shaded region fall within the interval 0 ≤ y ≤ 2

Now, from the subsequent picture appended we sketch the solid acquired by turning the concealed region about the y-axis.

For the cross-sectional area of the washer:

[tex]A (y) = \pi (outer \ radius)^2 - \pi ( inner \ radius )^2 \\ \\ A(y) = \pi (2y^)2- \pi (y^)^2 \\ \\ A(y) = 4 \pi y^2 - \pi y^4 \\ \\ A(y) = \pi( 4 y^2 -y^4)[/tex]

Finally, the volume of (solid) is:

[tex]V = \int^2_0 A(y) \ dy \\ \\ V = \int^2_0 \pi (4y^2 -y^4) \ dy \\ \\ V = \pi \int^2_0 (4y^2 -y^4) \ dy \\ \\ V = \pi \Big[\dfrac{4}{3}y^3 - \dfrac{y^5}{5} \big ] ^2_0 \\ \\ V = \pi \Big [ \dfrac{4}{3}(2)^3-\dfrac{2^3}{5} \Big ] \\ \\ V = \dfrac{64}{15}\pi \\ \\ V = (4.27 ) \pi[/tex]


[tex]1.8 greater \: or \: less \: than \: 18percent[/tex]
is 1.8 greater or less than 18% ​

Answers

It’s greater than 18%

Answer and explain please ill mark brainliest!!!!!!!!

Answers

Answer:

Yes, Elias got his food before reaching the potluck.

Step-by-step explanation:

Elias left home at 7:00 one morning, determined to make the ten-mile trip to Leaders on a bicycle. Soon thereafter, Elias' parent noticed he had forgotten his potluck dish on the kitchen table, got into the family car, and tried to catch up with the forgetful child. Elias had a fifteen-minute head start, and was pedaling at 12 mph, while the parent pursued at 30 mph. Was Elias reunited with his potluck food before reaching Leaders that day? If so, where? If not, at what time was the food delivered?

Let's set x as the time after the parent leaves as x (time after the first 15-minute headstart)

When the two meet, it means that the distance is equal. Remember, distance = time * speed.

Using this, we know that Elias had a 15-minute headstart at 12 mph, which means that he had 0.25 of an hour. Thus, Elias had a 0.25 * 12 mile headstart.

We can write this equation for the distance Elias traveled.

0.25 * 12 + 12 * x

And this equation for the distance his parent traveled.

30 * x

These equations need to be equal so that the two meet.

0.25 * 12 + 12 * x = 30 * x

Simplify.

3 + 12x = 30x

Subtract 12x from both sides.

3 = 18x

Divide both sides by 18.

x = 1/6

So, it took 1/6 of an hour, which is 10 minutes, for the parent and Elias to meet.

If Elias were to get the food before he reached the potluck, the distance he traveled (0.25 * 12 + 12 * x) needs to be less than 12.

Plug 1/6 in for x.

0.25 * 12 + 12 * 1/6 =

3 + 2 = 5

Elias traveled 5 miles before his parent met him.

So, Elias did get his food before reaching Leaders.

Just in case, let's double-check this answer.

Using the distance = speed * time formula, we know that time = distance/speed. Elias's parent had to travel 5 miles at 30 mph, so it would have taken 1/6 of an hour to drive 5 miles.

Elias traveled at 12 mph for 1/6 + 1/4 of an hour, so he traveled:

(1/6 + 1/4) * 12 =

(4/24 + 6/24) * 12 =

10/24 * 12 =

120/24 = 5 miles

Thus, the previous answer is right.

I hope this helps! Feel free to ask any questions!

Find the area of a circle that has a circumference of 12π in.

Answers

Answer:

a = 1.91

Step-by-step explanation:

12 = 2π(r)

12/2 = 2π(r)/2

dividing by 2

=

6 = π(r)

you then divide this by π, or 3.14

6/3.14 = π(r)/3.14

=

1.91

A washer and a dryer cost $596 combined. The washer costs $54 less than the dryer. What is the cost of the dryer?

Answers

Answer:

The washer costs 220 and the dryer costs 376! brainliest pls!

Step-by-step explanation:

3 (7/5x+4) -2 (3/2 - 5/4x)​

Answers

Answer:

I know the mixed number will be 1 because u subtracts that's all I know and just subtracts the fractions ok sorry

Answer:

[tex]6\frac{7}{10}x + 9[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex]3(\frac{7}{5}x + 4)-2(\frac{3}{2}-\frac{5}{4}x)[/tex]

[tex](3*\frac{7}{5}x) + (3 * 4) + (-2 * \frac{3}{2}) + (-2 * -\frac{5}{4}x)[/tex]

[tex]\frac{21}{5}x + 12 + \frac{-6}{2} + \frac{10}{4}x[/tex]

Step 2:  Combine Like Terms

[tex]12 - 3 + \frac{21}{5}x + \frac{5}{2}x[/tex]

[tex]9 + (\frac{21*2}{5*2}x + \frac{5*5}{2*5})[/tex]

[tex]9+(\frac{42}{10}x + \frac{25}{10}x)[/tex]

[tex]9+\frac{67}{10}x[/tex]

[tex]6\frac{7}{10}x + 9[/tex]

Answer:  [tex]6\frac{7}{10}x + 9[/tex]

Please let me know if you need to make it more clear!  :)

Sandy brought 64 dozen cookies to the bake sale. Alejandro brought
dozen fewer cookies than Sandy brought. Pierre brought 2 dozen
fewer cookies than Alejandro brought. How many dozen cookies
did Pierre bring?

Answers

Sandy - 64 dozens = 768 single cookies.
Alejandro - 62 dozens = 744 single cookies.
Pierre - 60 dozens = 720 single cookies.

Pierre brought 720 cookies. You solve this by understanding that one dozen = 12 and multiplying 12 by the given number of dozens each student brought to find out the exact amount of single cookies. Hope this helped !

At Store A, a 60-ounce bag of shelled walnuts costs $11.99. At Store B, a 4-pound bag of shelled walnuts costs $11.99. Shelled walnuts are a better deal at
Store A or Store B

Answers

Answer:

Store B

Step-by-step explanation:

2x3/12 as a fraction

Answers

Answer:

1/2

Step-by-step explanation:

2*3=6

6/12=1/2

Answer:

[tex]\frac{1}{2}[/tex]--> 1/2

Step-by-step explanation:

3x2=6. half of 12 is 6 and so you would make it 6/12 or aka 1/2

i need help with this pls.

Answers

Answer:

The answer is D

Step-by-step explanation:

Plug all of the numbers in and they all work with the problem.

need help ASAP! please answer

Answers

Answer:

c

a

Step-by-step explanation:

GEOMETRY!! Will give brainliest

Answers

Answer:

60

Step-by-step explanation:

(20x15)0.5

60 because you distribute the .5

Please help and show work

Answers

The answer should be X= 3.60m

Pls answer this for me​

Answers

Answer:

A) 216in squared

Step-by-step explanation:

6 / 2 = 3

4 * 3 = 12

12 * 2 = 24

5 * 12 = 60

60 * 2 = 120

6 * 12 = 72

24 + 72 + 120 = 216in^2

Hope this helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

MADD (Mother's Against Drunk Drivers) wishes to estimate the proportion of adult drivers that have run at least one red light in the last month. A poll is conducted on a simple random sample of adult drivers and it is found that out of 1251 adult drivers, 641 of them have run at least one red light in the last month. You will be finding a 90% confidence interval for the fraction of adult drivers that run at least one red light in the last month.
Check that the normality assumptions are met?
Interpret the confidence interval obtained.

Answers

Answer:

Normality assumptions are met.

The 90% confidence interval for the proportion of adult drivers that run at least one red light in the last month is (0.4892, 0.5356). The interpretation is that we are 90% sure that the true proportion of all adult drivers than ran at least one red light in the last month is between these bounds.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Out of 1251 adult drivers, 641 of them have run at least one red light in the last month.

This means that [tex]n = 1251, \pi = \frac{641}{1251} = 0.5124[/tex]

Normality assumptions:

We need that: [tex]n\pi[/tex] and [tex]n(1-\pi)[/tex] are 10 or greater. So

[tex]n\pi = 1251*0.5124 = 641[/tex]

[tex]n(1-\pi) = 1251*0.4876 = 610[/tex]

So the normality assumptions are met.

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5124 - 1.645\sqrt{\frac{0.5124*0.4876}{1251}} = 0.4892[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5124 + 1.645\sqrt{\frac{0.5124*0.4876}{1251}} = 0.5356[/tex]

The 90% confidence interval for the proportion of adult drivers that run at least one red light in the last month is (0.4892, 0.5356). The interpretation is that we are 90% sure that the true proportion of all adult drivers than ran at least one red light in the last month is between these bounds.

A pair of athletic shoes costs ​90$. If the inflation rate remains constant at 4​%, write an algebraic rule to determine the​ cost, c(t), of the shoes after t years. ​c(t) =

REALLY NEED THIS ANSWER

Answers

Answer:

c(t)=90+90×0,04t

c(t)=3,6t + 90

What is the measure of arc PSR? *

75 degrees
260 degrees
65
100

Answers

Answer:

it most likely would be 260 degrees

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