let H be the altitude from vertex C. Which proves the first equality in the law of sines​

Let H Be The Altitude From Vertex C. Which Proves The First Equality In The Law Of Sines

Answers

Answer 1

The sine law of triangles can be proved by dividing the triangle into right-triangles.

Option (c) proves the first equality in the law of sines

From the question, we have:

h equals to the distance from point C to segment AB

The sine of angle is:

[tex]\mathbf{sin(\theta) = \frac{Opposite}{Hypotenuse}}[/tex]

For angle at A, we have:

[tex]\mathbe{\theta = A}[/tex]

[tex]\mathbf{Hypotenuse = b}\\\mathbf{Opposite = h}[/tex]

So, we have:

[tex]\mathbf{sin(\theta) = \frac{Opposite}{Hypotenuse}}[/tex]

Substitute values for Opposite, Hypotenuse and theta

[tex]\mathbf{sin A = \frac{h}{b}}[/tex]

Similarly

[tex]\mathbf{sin B = \frac{h}{a}}[/tex]

Make h the subject

[tex]\mathbf{h = a\ sinB}[/tex]

Substitute [tex]\mathbf{h = a\ sinB}[/tex] in [tex]\mathbf{sin A = \frac{h}{b}}[/tex]

[tex]\mathbf{sin A = \frac{a\ sinB}{b}}[/tex]

Divide both sides by a

[tex]\mathbf{\frac{sin A}{a} = \frac{sinB}{b}}[/tex]

Hence, the correct option is (c).

Read more about proof of sine law at:

https://brainly.com/question/4637169


Related Questions




Write 1000 as a power of 10





Answers

10 to the power of 3 is the answer brainlist plz plz

Gus wrote the following riddle: I am a number between 30 and 60. My ones digit is three less than my tens digit. I am a prime number.

What number does Gus’ riddle describe?

Answers

Answer: 41

Step-by-step explanation:

Picture below! Plz, answer ASAP. Brainilest will be given!

Answers

Answer:

C

Step-by-step explanation:

just use calculator

When twelve is added to eight times a number, the result is one hundred and fifty. Find the
number.

Answers

Adding twelve eight times is the same as 12 x 8 which is 96

x + 96 = 150

To find 150, subtract 96 from both sides

x = 150 - 96
x = 54

A pair of adjacent angles that form a straight line

Answers

Answer:

it is called a linear pair.

mark brainliest pls

Answer:

lianer lines

Step-by-step explanation:

Can you please help me with#11?I'm not sure how to find the answer.​

Answers

Answer:

You need to find the x and y intercepts so...

The x intercept is (18,0) since x=18

The y intercept is (0,12) since y=12

Step-by-step explanation:

Cover the y when you are finding the y intercept

Cover the x when you are finding the x intercept

8x/8

144/8

=18

12y/12

144/112

=12

I think of a number Then multiply it by 3 then add 4 then divide by 4 my final answer is 3 less than the number is the number i thought of the beginning.

Write it as an equation and solve.

Answers

(3x + 4) / 4 = x - 3
3x + 4 = 4x - 12
-x + 4 = -12
-x = -16
x = 16

Check:
(3x + 4) / 4 = x - 3
(3*16 + 4) / 4 = 16 - 3
(48 + 4) / 4 = 13
52 / 4 = 13
13 = 13

For every five candy bars David sells, he earns $1. How many candy bars he sell to earn $15 please help​

Answers

Answer:

75

Step-by-step explanation:

5 candy bars =1 dollar what about 15 dollars

Answer:

75 candy bars

Step-by-step explanation:

because 15 x 5 = 75. we got 15 because that's the total amount of money he got and we got 5 because every 5 candy bars.

Có bao nhieu cách đổi một tờ tiền mệnh giá 200.000VNĐ thành các tờ tiền mệnh giá 50.000VNĐ,20.000VNĐ,10.000VNĐ

Answers

Answer:

madc'dsv wr;lja''vr3'fbfsh'tht'rth

Step-by-step explanation:

Plsssss Help i have no idea how to do this​

Answers

Answer:

500

Step-by-step explanation:

solve pls brainliest

Answers

Answer:

28.5

Step-by-step explanation:

1/2 is 0.5 as a decimal.

That would mean that 28 1/2 is the same as 28.5.

Hope this helps! Brainliest would be really appreciated!

28.5. Pls brainliest

Last year, the Galaxy Fair Amusement Park installed a family roller coaster they named The Twist. This coaster was designed to accommodate riders from age 4 to adult and features a tall climb hill and several banking turns. Overall, the park has been disappointed in the reception of The Twist, and very few families are riding the coaster this season. After some research, they discovered that park guests think the climb hill is too tall and fast for younger riders. Galaxy Fair Amusement Park has asked a roller coaster design firm to help them redesign The Twist during the coming off season. The quadratic function that represents the current climb hill is () = −0.102 + 3.6 − 2.4 and the quadratic function that represents the proposed redesign of the climb hill is () = −0.032 + 1.62 − 6.87. In these functions, the value of x represents the time, in seconds, since the roller coaster train cars have left the station, and the output variable is the height of the roller coaster track, in feet, above the ground. 1. Rewrite both () and () from standard form into vertex form. Explain your process. HINT: Each function has a common factor. Start by dividing it out. 2. State the vertex of each function. What does each vertex represent in context of The Twist? 3. Compare the a-value of () to the a-value of the parent quadratic function. What effect does this value have on a parabola? 4. Sketch both of the functions () and () on a single xy-plane. Describe the steps you took to create your sketch. 5. Use the vertex forms of () and () and the sketch you created in question 4 to describe the track changes that occur when the function that represents the climb hill is altered from () to (). Do you think these changes will help younger riders better enjoy The Twist? Explain.

Answers

Omg no lol a las autoridades del estado y a la prensa local el pasado domingo por el grupo a las autoridades del departamento del interior del estado en el estado del país en la capital mexicana y que se encuentra a un lado del país y a las autoridades del estado a las que no se ha podido hacer el

Answer:

can you add a picture or summerize this

Step-by-step explanation:

Use the number line to find the difference of 3 - (-1.5)

Answers

your answer is 4.5 you're welcome :-)

Answer:4.5

Step-by-step explanation:

the rule is

positive - negative  changes to positive + positive so

3- (-1.5) changes to 3 + 1.5 which equals 4.5

What is the length of side s of the square shown below? 45° 6 30
A. 34
B. 6
C. 3
D. 6-2
E. 2
F. VE​

Answers

Answer:

The correct answer should be D.

Step-by-step explanation:

Express the following rate as a unit rate: 28 1/3 minutes to run 3 1/3 miles​

Answers

Answer:

28.20

Step-by-step explanation:

60 seconds in a minute

1/3 of a minute is 20 seconds

“In any given triangle, the square of the longest side is equal to the sum of the squares of the two shorter sides.” a. 5 cm, 12 cm, 13 cm b. 4 cm, 5 cm, 7 cm c. 3 cm, 4 cm, 5 cm d. 9 cm, 12 cm, 15 cm

Answers

The statement "the square of the longest side is equal to the sum of the squares of the two shorter sides" is true for a right-angled triangle.

(a) 5 cm, 12 cm and 13 cm

The statement is represented as:

[tex]\mathbf{13^2 = 12^2 + 5^2}[/tex]

[tex]\mathbf{169= 144 + 25}[/tex]

[tex]\mathbf{169= 169}[/tex]

Hence, the statement is true for triangle (A)

(b) 4 cm, 5 cm and 7 cm

The statement is represented as:

[tex]\mathbf{7^2 = 5^2 + 4^2}[/tex]

[tex]\mathbf{49 = 25 + 16}[/tex]

[tex]\mathbf{49 = 41}[/tex]

Hence, the statement is not true for triangle (B)

(c) 3 cm, 4 cm and 5 cm

The statement is represented as:

[tex]\mathbf{5^2 = 4^2 + 3^2}[/tex]

[tex]\mathbf{25 = 16 + 9}[/tex]

[tex]\mathbf{25 = 25}[/tex]

Hence, the statement is true for triangle (C)

(d) 9 cm, 12 cm and 15 cm

The statement is represented as:

[tex]\mathbf{15^2 = 12^2 + 9^2}[/tex]

[tex]\mathbf{225 = 144 + 81}[/tex]

[tex]\mathbf{225 = 225}[/tex]

Hence, the statement is true for triangle (D)

Read more about triangles at:

https://brainly.com/question/19182121

Can someone please help as I'm not sure how to tackle this step by step? Especially question b, d, g, j, k, l. Not how sure to do it if contains a surd just on its own.

Answers

Step-by-step explanation:

√a = 1√a so we can solve them easily:

b) 3√7 -√7= 3√7 - 1√7 =( 3-1)√7= 2√7

d) 5√6 - 2√6+√6= (5-2+1)√6 = 4√6

g) √2+2√2= 3√2

j) √5+5√5 - 3√5 = 3√5

k) 2√3 + √3 - 5√3= -2√3

I) 5√11 + 7√11 - √11 = 11√11

‼️PLEASE HELP I HAVE NO IDEA ON HOW TO DO THIS‼️‼️

Solve each system by elimination. Please show the work.

1. 3x+3y+6z=9; 2x+y+3z=7; x+2y-z=-10

2. 3x-y+z=3; x+y+2z=4; x+2y+z=4

3. x-2y+3z=12; 2x-y-2z=5; 2x+2y-z=4

Answers

Answer:

under what topic is this?

A cylinder with a radius of 10ft has a volume of 2, 198.0013
What is the height of the cylinder

Answers

Answer:

~7 ft

Step-by-step explanation:

2,198.0013 = pi × 10^2 × h

h = 2198.0013 / (3.1416 × 100)

h = 6.996 ft ~ 7 ft

A sample survey of discount brokers showed that the mean price charged for a trade of shares at per share was . The survey is conducted annually. With the historical data available, assume a known population standard deviation of . a. Using the sample data, what is the margin of error associated with a confidence interval (to decimals)

Answers

Using the z-distribution, it is found that the margin of error of the confidence interval is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In this problem, it is stated that the population standard deviation is known, thus, the z-distribution is used.

The margin of error of a z-confidence interval is given by:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

z is the critical value. [tex]\sigma[/tex] is the population standard deviation. n is the sample size.

A similar problem is given at https://brainly.com/question/25214883

Any helpp? someone....?

Answers

Answer:

I think that the speed is 65mph, because there is the largest number of people on the graph for 65mph.

Step-by-step explanation:

What is the algebraic inverse of the function f(x) = 5x - 15?

VIEW IMAGE PLEASE!

Answers

Answer:

B

----------------------

answer question right or else

Answers

Answer:

60

Step-by-step explanation:

yes, it's a question

have a great day

the answer to your question is 60, i found this by taking 30/1 multiplied by 5/100

i need help with this question

Answers

Answer:

below

Step-by-step explanation:

I'm not absolutely know what are you asking for the answer, but this graph shows ...

The first 20 minutes he has a constant speed of 1.8/20=0.09 km/min progress to 1.8 km away from home, then has 10 minutes (from 20-30) stop at the spot.

Then he drive home with speed of 0.045 km/min (1.8/40=0.045) for 40 minutes to return to the start point.

8 × 4/8 =
patulong po​

Answers

Answer:

4

Step-by-step explanation:

the answer is 4

yep it is because eight cancels out with the other one

Answer:

(8 × 4)/8

so answer=4

Triangle ABC has vertices A(-3,2) B(0,1) and C(-2,-3).
1. Graph triangle ABC and its reflection across the line x=-2?
2. What are the coordinates of triangle A'B'C' if triangle ABC is reflected across the x-axis?
3. What are the coordinates of triangle A'B'C' if triangle ABC is reflected across the y-axis?
4. What are the coordinates of triangle A'B'C' if triangle ABC is reflected across the line y=x?

Answers

If triangle ABC is reflected across the line x = -2, the new point is A'(-1, 2), B'(2, 1) and C'(-2, -3)

If triangle ABC is reflected across the x axis, the new point is A'(-3, -2), B'(0, -1) and C'(-2, 3)

If triangle ABC is reflected across the y axis, the new point is A'(3, 2), B'(0, 1) and C'(2, -3)

If triangle ABC is reflected across the line y = x, the new point is A'(2, -3), B'(1, 0) and C'(-3, -2)

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Triangle ABC has vertices A(-3,2) B(0,1) and C(-2,-3).

1) If triangle ABC is reflected across the line x = -2, the new point is A'(-1, 2), B'(2, 1) and C'(-2, -3)

2) If triangle ABC is reflected across the x axis, the new point is A'(-3, -2), B'(0, -1) and C'(-2, 3)

3) If triangle ABC is reflected across the y axis, the new point is A'(3, 2), B'(0, 1) and C'(2, -3)

4) If triangle ABC is reflected across the line y = x, the new point is A'(2, -3), B'(1, 0) and C'(-3, -2)

Find out more on transformation at: https://brainly.com/question/1620969

Simplify this please: ^4√y^20

Answers

Answer: y^5

Step-by-step explanation:

In the picture

At its peak, an online shopping site was selling about 420 items per second. At this rate, how many items would it sell in 30 minutes ( 1,800 seconds)?

Answers

756,000

You multiply the number of items by the number of seconds

Answer: 758,000

Step-by-step explanation:

Expression: 420 x 1,800

Basically just find the number of seconds and since every second 420 items are sold just multiply 420 x number of seconds which is 1,800

PLEASE, I need help ASAP !

Answers

Answer:

I'm not 100% sure but I think it's C.

it might also be B. it's one of those 2 for sure but I'm like %80 sure it’s C.

Step-by-step explanation:

please let me know if im right or wrong....

Use the results from a survey of a simple random sample of 1176 adults. Among the 1176 respondents, 77% rated themselves as above average drivers. We want to test the
claim that
7/10 of adults rate themselves as above average drivers. Complete parts (a) through (c)
a. Identify the actual number of respondents who rated themselves as above average drivers
(Round to the nearest whole number as needed)

Answers

Using the sample data to test the hypothesis, we have that:

The actual number of respondents who rated themselves as above average drivers is 906.The p-value of the test is 0, which is less than the standard significance level of 0.05, thus we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.7.

77% of the sample of 1176 adults rated themselves as above average drivers, that is:

[tex]0.77(1176) = 906[/tex].

Thus, the actual number of respondents who rated themselves as above average drivers is 906.

At the null hypothesis, we test if the proportion is [tex]\displaystyle \frac{7}{10} = 0.7[/tex], that is:

[tex]H_0: p = 0.7[/tex]

At the alternative hypothesis, we test if the proportion is greater than 70%, that is:

[tex]H_1: p \geq 0.7[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested.n is the size of the sample.

In this problem, the parameters are [tex]\overline{p} = 0.77, p = 0.7, n = 1176[/tex].

Thus, the value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.77 - 0.7}{\sqrt{\frac{0.7(0.3)}{1176}}}[/tex]

[tex]z = 5.24[/tex]

The p-value of the test is the probability of finding a sample proportion above 0.77, which is 1 subtracted by the p-value of z = 5.24.

Looking at the z-table, z = 5.24 has a p-value of 1.

1 - 1 = 0.

The p-value of the test is 0, which is less than the standard significance level of 0.05, thus we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.7.

A similar problem is given at https://brainly.com/question/24330815

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