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).

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Related Questions

Suppose 1.5 liters of water come out of a faucet each minute. For how many minutes was the faucet on if 18.6 liters of water came out?

Answers

Answer:

It was on for 12.4 minutes

Step-by-step explanation:

Answer:

12.4

Step-by-step explanation:

rate of water = 1.5x

x = amount of time

18.6 = 1.5x

x = 12.4

What are the two cases for 丨4x - 1丨= 19?

Answers

Answer:

Step-by-step explanation:

x = 5

Answer:

x=5 and -17/4

Step-by-step explanation:

The two equations for 丨4x - 1丨= 19 is

4x-1=19

and

4x-1=-19

So for 4x-1=19

4x=20

x=5

4x-1=-18

4x=-17

x=17/4

Hope this helps!

Yolanda has 2 gallons of water in a bucket. If she throws out 2/3 of water, how much water will shr have left?

Answers

It will be left 1/7 I think it will work

Answer:

1.33333333333

Step-by-step explanation:

2-(2/3)= 1.33333333333

The. Problem I in the picture

Answers

Answer:

can't see it clearly sorry about that

What is the domain of y=log 4(x+3)?

Answers

All the real number less than -3. It the first one hope this help

Answer:

Y= log 4(x+3)

then you should do (x+3)= 3x= log 4.

Step-by-step explanation: Sorry I'm not 100 % sure so yeah

But let's see 3x  =  log 4

oh so then you need to divide 3 at both sides so then what's 4/3= 1.3333333333.

So now I think it's C). All real numbers are les than 3.

The table lists recommended amounts of food to order for 25 party guests. and are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering​ purposes, they will count each of these​ 45 "drop-in" guests as half a guest. How much of each food item should and order for a graduation party with ​drop-in guests?

Answers

Answer:

667

Step-by-step explanation:

Answer:

It will be

1. 3

2.2

3.5

Step-by-step explanation:

HOpe this helps!

PLEASE HELP
WILL MARK BRAINLIEST
(don’t put links or i will report)


What type of correlation is shown within your data? Explain how you know.

Answers

Answer:

it looks like a positive correlation?

Step-by-step explanation:

I really don't know much but it looks like the y in increasing in a positive direction when the x is as well

Select the correct answer.
An archway is modeled by the equation y = -2x2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B?

A.
8 units

B.
6 units

C.
5 units

D.
3 units

Answers

Answer:

D. 3 units

Step-by-step explanation:

after you add you get a another number you make a another unit and get your answer or you can get the answer of the another number and add it to together.

that what I think it is

The width of a rectangular rug is 4 1/4 inches longer than twice its length. If the perimeter of the rug is 56 1/2 inches, which equation represents this situation?

Answers

The question requires calculating the perimeter of the rectangular r ug

The equation which represent the situation is 113/2 = 6x + 34/4 and length is 8 inches and width is 20 1/4 inches

Given:

let

length of the rectangular r ug = x inches

Width of a rectangular r ug = (2x + 4 1/4) inches

Perimeter of the r ug = 56 1/2 inches

Perimeter of the r ug = 2(length + width)

56 1/2 = 2{x + (2x + 4 1/4)

113/2 = 2(x + 2x + 17/4)

113/2 = 2(3x + 17/4)

113/2 = 6x + 34/4

113/2 - 34/4 = 6x

(226-34) / 4 = 6x

192/4 = 6x

48 = 6x

divide both sides by 6

x = 48/6

x = 8 inches

So,

length of the rectangular r ug = x inches

= 8 inches

Width of a rectangular r ug = (2x + 4 1/4) inches

= 2(8) + 4 1/4

= 16 + 4 1/4

= 20 1/4 inches

Therefore, the equation which represent the situation is 113/2 = 6x + 34/4 and length is 8 inches and width is 20 1/4 inches

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If this is the graph of f(x)= a(x+h) +k, then:

Answers

Answer:

The forth one as both are positive  the domain  =  x ascending = + h and the range = y  where y = k the vortex and both include infinity

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Apie

answer I'll give brainliest to first one
10 points​

Answers

Answer:

Have a splendiferous day...

Step-by-step explanation:

3÷12=¼

6÷10=⅗

7÷14=½

10÷11=⅚

2÷4=½

4÷16=¼

3÷24=⅛

18÷54=⅓

Answer:

1) 3÷12=[tex]\frac{1}{4}[/tex]

2) 6÷10=[tex]\frac{3}{5}[/tex]

3) 7÷14=[tex]\frac{1}{2}[/tex]

4) 10÷12=[tex]\frac{5}{6}[/tex]

5) 2÷4=[tex]\frac{1}{2}[/tex]

6) 4÷16=[tex]\frac{1}4[/tex]

7) 3÷24=[tex]\frac{1}{8}[/tex]

8) 18÷54=[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Hope this helps have a great day ahead! Have a great Halloween :) Tell me if im wrong please <3

f(x) = 2x + 1
Graph 2f(x) - 3

Answers

Answer:

(Hope this helps can I pls have brainlist (crown)☺️)

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope:  2

x- intercept [tex](-\frac{1}{2}),0[/tex]

y-intercept:  ( 0 , 1 )

Graph in pic

(Credit: M a t h w a y

Find the value of a that satisfies the following

P(Z>a)=0.9207

Answers

Answer:

-1.409

Step-by-step explanation:

I’m assuming this a z-score for stats. You would just go into your calculator, in my case a Casio. Then, you’d press on the stats module, click F5 (DIST), F1 (NORM), F3 (InvN). You would change the data to variable, then put in tail right, area .9207, SD 1, mean of 0. Then hit execute and you’ll get the answer of -1.4097958. Round it if needed.

Solve for n.
ples help me solv for n

Answers

Answer: 50 miles per hour

Step-by-step explanation: It is that because when the line passes on the one hour mark it is 50.

Please help!

Triangle ABC has angle measures as shown. Show work. Complete sentence.




(a) What is the value of x?








(b) What is the measure of angle CBA?




(c) What is the measure of angle CAB?




(d) When these 3 interior angles of a triangle are added together, what does it equal?

Answers

9514 1404 393

Answer:

  (a) x = 22

  (b) 46°

  (c) 44°

  (d) 180°

Step-by-step explanation:

Because the sum of the interior angles of a triangle is 180°, we know that the sum of the acute angles in a right triangle is 90°.

(a)

The sum of the marked acute angles is 90°.

  2x +(3x -20) = 90

  5x = 110 . . . . . . . . . . add 20, collect terms

  x = 22 . . . . . . . . . divide by 5

__

(b)

∠CBA = (3x -20)° = (3·22 -20)° = 46°

__

(c)

∠CAB = 2x° = 2(22)° = 44°

__

(d)

The sum of a triangle's interior angles is 180°.

help me with this math question WILL GIVE BRAINLIEST

Answers

Step-by-step explanation:

all such triangles inscribed into a circle with their baseline being the diameter of the circle, must be right-angled. the 90 degree angle is at C.

the other thing is that the sum of all angles in a triangle is always 180 degrees.

so,

B = 180 - 90 - 20 = 70 degrees

Writing Describe another method
for solving the expression in
Exercise 1. Does this method always
work? Explain.

Answers

Answer: pontos livres

Step-by-step explanation:

o cachorrinho wwss veyry rápido

Please explain why 31% is the answer

Answers

9514 1404 393

Answer:

  b)  31%

Step-by-step explanation:

95% of the normal distribution is between Z values of ±1.96.

99% of the normal distribution is between Z values of ±2.576.

The change from a 95% interval to a 99% interval widens the range by ...

  (2.576/1.96 -1) × 100% ≈ 31.4%

The width of the interval increases about 31%.

__

Compare the two attachments. The tail area of 0.05 means the central area is 0.95. Similarly, the tail area of 0.01 means the central area is 0.99.

_____

Additional comment

As always, when you're dealing with percentages, you need to understand what the base value is. Here, when we're talking about 95% and 99% confidence intervals, we're not talking about the numbers 0.95 and 0.99 and the increase from 0.95 to 0.99.

Rather we're talking about areas under the normal probability distribution curve, and the Z-values associated with those intervals. The change in interval width refers to the change in Z-values associated with the areas of 0.95 and 0.99.

Jake has a wooden board that measures 8.25 feet long. He cuts the board into pieces that each measure 0.75 foot so he can make signs. If Jake earns $15.95 for each sign he sells, how much money can he earn from the signs he makes with this board?

Answers

Step-by-step explanation:

Answer:

Jake cuts the board into pieces that measure .75 feet each. Before cutting the board, it is 8.25 feet long. So, we must divide 8.25/.75 to find out how many pieces of board jake cut.

8.25/.75= 11 pieces

Since he makes $15.95 per sign, and there are 11 signs, we must multiply 15.95 by 11. This is equal to 175.45.

Therefore, jake can earn $175.45

Step-by-step explanation:

Can you give me brainliest?

6 miles in 2 hours how fast you go

Answers

Speed is presented as miles per hour (mph) or kilometres per hour (kmph). To take the above example: You walk 6 miles in 2 hours. 60/20 = 3mph.

Answer: 3mph
You would be going 3mph

Steffan cycled 10km in 45 minutes. He rested for
20 minutes then cycled a further 8 km in 40 minutes.
Work out his average speed for the whole journey.M
Give your answer correct to one decimal place.


Math

Answers

Answer:  If you measure out a 10k course and then time how long it takes you to ride it, that will tell you which speed range to use and what time to input. If you weigh 185 pounds and fall into the 12 to 13 mph range, it will take you about 30 minutes to pedal 10k — which means that according to the ACE estimates, you will burn about 335 calories.

Step-by-step explanation:

Hope this helps!

Answer:

0.2km/min or 12.7km/hour

Step-by-step explanation:

speed = distance ÷ time

speed = (10km + 8km) ÷ (45 mins + 40 mins)

= 18 ÷ 85

= 0.21176...km/min ≈ 0.2km/min

To convert 0.21176...km/min into km/hr, you multiply by 60

0.21176...km/min × 60 = 12.70588...km/hr ≈ 12.7km/hr

Solve : (6a -5b -8c) - ( 15b + 2a - 5c)

Answers

Answer:

4a - 20b - 3c

Step-by-step explanation:

6a - 5b - 8c - 15b - 2a + 5c

= 4a - 20b - 3c

I HOPE IT WILL HELP YOU.

Thank you.

I HOPE YOUR DAY GOES GREAT.

A polygon is shown on the graph:

A polygon is shown on the coordinate plane. Vertices are located at 3 comma 5, 1 comma 3, 1 comma 1, 2 comma 0, 4 comma 0, 5 comma 1, and 5 comma 3.

What effect will a translation 3 units down and 2 units left have on the polygon? Be sure to address how it could impact the angles, side lengths, and congruency between the original pre-image and the image.

Answers

9514 1404 393

Answer:

  angles, side lengths, and congruency are unaffected by translation: translated figures are congruent.

Step-by-step explanation:

The proposed transformation is ...

  (x, y) ⇒ (x -2, y -3) . . . . . . translation 2 left and 3 down

Translation, rotation, and reflection are all "rigid" transformations. They do not affect any measure of a figure: angles, side lengths, area all remain the same after any of these transformations. The figure after any of these transformations, or any combination of them, is congruent to the original.

__

The attachment shows the original figure (brown) and the translated figure (red). The pre-image and the image are congruent.

Answer: goood answer

Step-by-step explanation:

Help help please please

Answers

Answer:

165km

Step-by-step explanation:

if 1cm on the map = 15km,

then since 11cm is 11x 1, we multiply the kilometers by 11, getting 165km.

Given that [tex]I_0 = 10^-12[/tex] watts/[tex]meters^2[/tex], what is the intensity of a sound for which the decibel level of the sound measures 156? Round off your answer to three decimal places.

Answers

The intensity of sound which the decibel level of the sound measures 156 is 3.981 × 10³ W/m²

Decibel level, dB = 10log₁₀(I/I₀) where dB = decibel level = 156, I = intensity at 156 dB and I₀ = 10⁻¹² W/m².

Since we require I, making I subject of the formula, we have

dB/10 = log₁₀(I/I₀)

[tex]\frac{I}{I_{0} } = 10^{\frac{dB}{10} } \\I = I_{0} 10^{\frac{dB}{10} }[/tex]

Substituting the values of the variables into the equation, we have

[tex]I = I_{0} 10^{\frac{dB}{10} }\\I = 10^{-12} 10^{\frac{156}{10} }\\I = 10^{-12} 10^{15.6}\\I = 10^{15.6-12} \\I = 10^{3.6} W/m^{2}[/tex]

I = 3981.072W/m²

I = 3.981 × 10³ W/m²

So, the intensity of sound which the decibel level of the sound measures 156 is 3.981 × 10³ W/m²

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Sorry I ain’t know why it look like that buh can someone help asap

Answers

Answer:

[tex]for \: \: dmain \: of \: {f}^{ - } \: \: is \: equal \: f \: range \\ y = \sqrt{x } - 5 \\y \: range \: is \: y \geqslant - 5\\ y + 5 = \sqrt{x} \\ x = {(y + 5)}^{2} \\ {f}^{ - 1} = {(x + 5)}^{2} \\ \\ dmain \: of \: \: {f}^{ - 1} \: x \geqslant - 5[/tex]

When you divide two fractions is the quotient always smaller than the dividend?

Answers

A fraction can really look like anything. So the quotient can be sometimes larger than the dividend.

A new car sells for $27,300. It exponentially depreciates at a rate of 6.1% to $22,100. How long did it take for the car to depreciate to this amount? Round your answer to the nearest tenth of a year. fill in the blank 1

Answers

Answer:

3

Step-by-step explanation:

27300 * (1-6.1%)^n = 22100,

n∈(3,4)

when n = 3,≈22603;

when n = 4,≈21224;

so choose n = 3.

Therefore, it takes  car to depreciate to this amount is [tex]3[/tex].

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

A new car sells for $[tex]27,300[/tex]. It exponentially depreciates at a rate of [tex]6.1[/tex]% to $[tex]22,100[/tex].

So, the equation is

[tex]27300(1-6.1)^n=22100\\\\[/tex]

when [tex]n[/tex] belongs to [tex](3,4)[/tex]

when [tex]n=3\\[/tex]

The equation would be

[tex]27300(1-6.1)^3=22100\\\\=22603[/tex]

When

[tex]n=4\\27300(1-6.1)^4=22100\\=21224[/tex]

So, the time it takes to depricate to the given amount is [tex]22603[/tex] when [tex]n=3[/tex].

Hence, it takes  car to depreciate to this amount is [tex]3[/tex].

To know more about the simplification

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Three consecutive integers have a sum of 45. Find the integers.

Answers

Answer:

14,15,16

Step-by-step explanation:

Call n the first integer so you get:

n+(n+1)+(n+2)=45

3n+3=45

3n=42

n=14

The integers are:

14,15,16

Answer:

14,15,16

Step-by-step explanation:

Let the integers be x, (x+1),(x+2)

So,

x+(x+1)+(x+2)=45

x+x+1+x+2=45

3x+3=45

3x=45-3

x= 42/3

x=14

Now put the value.

x= 14(x+1)= 14+1= 15(x+2)=14+2= 16

Now, Add these integers

you'll get

14+15+16=45

jim dog eats 11/3 bones in five days how many bones will the dog eat in 12 days

Answers

Answer:

The answer would be 44

Step-by-step explanation:

First, you have to simplify the improper fraction, that would make the it a mixed number which would be 3 2/3. When 3 2/3 is multiplied by 12 is 44. Hope this helps!

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