In the triangle shown above, m∠B = 105°, a = 12 in, and c = 8 in. What is the approximate length of side b?
A.
257.69 in
B.
14.44 in
C.
15.26 in
D.
16.05 in

Answers

Answer 1

Answer:

Step-by-step explanation:

Since we have one angle with an opposite side and another side known, we are dealing with an ambiguous case. There are either

0

,

1

or

2

solutions to this triangle.

We start by determining the measure of

A

using the law of Sines, since we already know the measure of side

a

.

sin

A

a

=

sin

B

b

sin

A

14

=

sin

105

˚

23

A

=

arcsin

(

14

sin

105

˚

23

)

A

=

36

˚

There is only one solution to this triangle, because if it was, then the alternative measure of A would be

180

˚

36

˚

=

144

˚

, which when added to

B

, would make the sum of the angles in the triangle exceed

180

˚

.

We can now use the measure of angles

A

and

B

to solve for angle C.

A

+

B

+

C

=

180

˚

36

˚

+

105

˚

+

C

=

180

˚

C

=

39

˚

The last step is using this information to reapply the law of sines and determine the length of side

c

.

sin

B

b

=

sin

C

c

sin

105

˚

23

=

sin

39

˚

c

c

=

23

sin

39

˚

sin

105

˚

c

=

15

In summary

The triangle has the following measures.

A

=

36

˚

a

=

14

units

B

=

105

˚

b

=

23

units

C

=

39

˚

c

=

15

units

Hopefully this helps!


Related Questions

Find the sum of−3x^2

Answers

Answer:

[tex]x+y=2[/tex]

[tex]y=-x+2[/tex]

[tex]slope (m)=-1[/tex]

[tex]slope ~of ~perpenddicular ~line:-[/tex]

[tex]-1/m_{2}[/tex]

[tex]\frac{-1}{-1} =1[/tex]

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

hope it helps...

have a great day!

19.05 divided by N = 12.7

Answers

Answer:

1.5

Step-by-step explanation:

19.05 divided by 12.7 = 1.5

Answer:

1.5

Step-by-step explanation:

19.05 divided by 12.7 = 1.5

A company rents out 18 food booths and 27 game booths at the county fair. The fee for a food booth is $50 plus $6 per day. The fee for a game booth is $65 plus $8 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid.

Answers

Answer:

$2655 + $324d

Step-by-step explanation:

total cost of a booth = fixed cost + (variable cost x number of days)

Fixed costs are costs that do not vary with output

Variable costs are costs that vary with production

cost of 18 food booths = 18(50 + 6d) = 900 + 108d

cost of 27 game booths = 27(65 + 8d) = 1755 + 216d

Add the total cost of the food and game booths together 900 + 1755 = 2655

108d + 216d = 324d

PLZ HELP
In ⊙C, DE ≅ FG, Which statement must be true? Select all that apply.

Answers

Answer:

E because is covered all angle

< DCE ≅ < GCF must be true

Hence Option A and E are true statements.

What are angles of circle?

A circle has a total of 360 degrees all the way around the center, so if that central angle determining a sector has an angle measure of 60 degrees, then the sector takes up 60/360 or 1/6, of the degrees all the way around. In that case, the sector has 1/6 the area of the whole circle.

According to the given figure:

DE ≅ FG

So < DCE ≅ < GCF must be true

Because DE ≅ FG

< DCE ≅ <GCF is similar to DE ≅ FG

Hence, < DCE ≅ < GCF must be true

Hence Option A and E are true statements.

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Help pls lol





Ahiwbsianaikebdoansijahdiwkanjdjsbfjnsbdjebjfjf

Answers

Answer:

the perimeter of this trapzoid is 26.5.

Sorry if I am wrong and please do correct me if I am wrong.

Step-by-step explanation:

Review the graph of function f(x). On a coordinate plane, a curve starts at closed circle (negative 2, 2), curves down to (negative 1, 1), and curves up through (0, 2) to closed circle (3, 6). Using the extreme value theorem, what are the minimum and maximum values of f(x)? minimum value = 1; maximum value = 6 minimum value = 2; maximum value = 6 minimum value = –1; maximum value = 3 minimum value = –2; maximum value = 3

Answers

Answer:

A. minimum value = 1; maximum value = 6

Step-by-step explanation:

Correct on Edge 2021

if the probability of rain tomorrow is 0.15 what is the probability that it will not rain​

Answers

Answer:

85% or 99.85%

Step-by-step explanation:

If you mean 15% by 0.15 then the probability that it will not rain is 85% because, 100-15=85.

If you mean 0.15% by 0.15 then the probability that it will not rain is 99.85% because, 100-0.15 is 99.85.

1.3. If Sara draws a red ball and DOES NOT RETURN it, and then she goes to draw a green
ball, is this considered a dependent or independent event?

Answers

Answer:

Dependent Event

Step-by-step explanation:

Assume that are 10 balls, such that:

[tex]Red = 6[/tex]

[tex]Green = 4[/tex]

If the balls are replaced after taken, the probability is:

[tex]Pr(Red) = 6/10[/tex]

[tex]Pr(Green) = 4/10[/tex]

This is referred to as independent event; because each selection do not affect the next or previous selection

However, if the balls are not replaced, the probability is:

[tex]Pr(Red) = 6/10[/tex]

[tex]Pr(Green) = 5/(10 - 1) = 5/9[/tex]

We subtracted 1 because there is a reduction in the number of balls when the red ball is not returned.

This is referred to as independent event; because a selection affects the next selection

Which values make this inequality true?

Answers

Answer:

2

Step-by-step explanation:

2-2=4 which is equal to 4

At a restaurant grand opening, a giant sandwich that was 352 centimeters long was divided equally among 22 people. Clyde got one of the pieces, ate half, and saved half for later. Which equation can we use to estimate the length of the piece of sandwich Clyde saved?

Answers

Answer:

8 cm

Step-by-step explanation:

You neglected to include any equations

Here is one way to solve:

length of each piece

352/22 = 16

Half a piece

16/2 = 8

Choice C

352/22/2 = l

Answer:

352 ➗ 22 ➗ 2 = l

Step-by-step explanation:

Write an explicit formula for the following sequence. Find the fifteenth term.
10, 11, 12, 13, 14, ...

Answers

Answer:

Tn=n+9

Step-by-step explanation:

Tn=n+9

T15=15+9

T15=24

which expressions are equivalent to 4-3 over 4-1

Answers

Answer:

B

cause when dividing you are subtracting the exponents

so it 4^-3+1 = 4^-2

you shouldnt have negative exponents

so you flip it, which become 1/4^2

Hope that answers your question

Don't hesitate to comment if you are confused about something

Step-by-step explanation:

PLSSSSSSSSSSSSSSSSSSSSS HEEEEEELP

Answers

Answer:

notice the two angles are vertical to each other making them equal to each other

for the first angle add 45 and 15 together to get 60

set 60 = 4x (the other angle using the vertical angle congruence theorem)

solve for x gives us 15

Step-by-step explanation:

In parallelogram MNPT, IZM= (6x + 10)° and
mZN= (5x + 10.5)° . How many degrees is ZT?

Answers

Answer:

83 degrees

Step-by-step explanation:

We can use the consecutive angle theorem to find the the value of x.

We can do that by doing 5x+10.5+6x+10 = 180

After simplifying, we get 11x+20.5=180

Subtract 20.5 on both sides and you get 11x=159.5.

Divide by 11 on both sides and you get x=14.5

Now we can use opposite angle theorem and set angle N and angle T equal.

That means we could write 5x+10.5 = m<T

We can substitute 14.5 for x and we get 72.5+10.5 = m<T

Simplify and you get 83 = m<T

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

Hope this helps!

For each set of angles or sides lengths, determine whether they could form a unique triangle, more than one triangle, or no triangle.

5 cm, 10 cm, 12 cm

8 ft, 12 ft, 20 ft

40°, 50°, 80°

28°, 51°, 101°​

Answers

Answer: They can form one triangle.

Step-by-step explanation: Since all triangle must have 180 degrees, there’s only one set of degrees that sum up to 180.

28+51+101=180

I’m sorry, but the feet/centimeters part you have to solve on your own. Remember, this is a learning community! No stress :) I can guarantee you won’t get it wrong though.

There’s many different triangles, and I’m sure from these feet/centimeters you can make at least one of the listed: Scalene (none of the sides are equal), isosceles (only 2 sides are equal) or equilateral triangle (all sides are equal). There’s also right triangles (which are triangles with one right angle also known as 90 degrees) that are either isosceles or scalene or both! Try your best and remember, no stress :)

PLEASE ANSWER ME AS FAST AS POSSIBLE

THANK YOU!

Answers

Answer:

5/8 - 1/4

Step-by-step explanation:

because it makes more sense I don't know how to explain

Answer:

4th option.

Step-by-step explanation:

The number getting subtracted is 5/8 since there are 5 boxes shaded in.

The number subtracting from it is 2/8 but that is not an option so the only other option equivalent to 2/8 is 1/4.

5/8 - 1/4 = 3/8 so the answer would also need to include 3/8 as the difference.

The only choice with all this is the 4th one

agles
1. Find the measure of arc ABC
110 °


Answers

Answer:

Arc ABC = 250°

Step-by-step explanation:

m<AOB = 110° (given)

Based on the central angle theorem, central angle m<AOB equals the intercepted arc AB

Therefore,

m<AOB = measure of arc AB = 110°

Thus:

Arc ABC = 360° - arc AB (Full circle = 360°)

Arc ABC = 360° - 110°

Arc ABC = 250°

The dot plots compare the number of raffle tickets sold by boys and girls during a school fund-raiser. Which plot has an outlier?

Answers

Answer:

Girl's plot

Step-by-step explanation:

The exact question is as follows :

Given - The dot plots compare the number of raffle tickets sold by boys and girls during a school fund-raiser.

To find - Which plot has an outlier?

Proof -

The correct answer is - Girls

Reason -

Girls plot has an outlier because values way outside the majority of the data.

Definition of outlier -

A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data.

Here in the Girl's plot we can see that, all the dots are close but there is one dot that is lies outside

But in Boy's plot all the dots are close to each other , no dot is lies outside to any other dots.

So,

The correct option is -

Girl's plot has an outlier.

The double cone is intersected by a vertical plane passing through the point where the tips of the cones meet. What is the shape of the cross
section formed?

Answers

Is there any like math or equations??

Anna enjoys dinner with her family at a restaurant in Washington, D.C. She leaves a 15% tip on the price of her meal. She also has to pay a 10% sales tax on her meal, which is calculated on the pre-tip amount. She spends a total of $27.50 for dinner, including tax and tip. What is the cost of her dinner without tax and tip? Show your work.

Answers

Answer:

$22

Step-by-step explanation:

tax and the tip increase the price paid for the meal

she paid 15 + 10 = 25% more than the price of her meal

p = original price

1.15 x p = 27,50

p = 27.50 / 1.15 = 22

Two-Way Tables Laura wants to know whether the top golfers in the world tend to be American. To do this, she searches the Internet to find the current top-20 male golfers and top-20 female golfers and records whether they are American. This two-way table shows her data. Keep the two way table window open as you work on the tasks. Part A Find the relative frequencies by rows.

Answers

Answer:

                      Male                   Female            Total

American 11/17 = 0.647  l 6/17 = 0.353 l 17/17 = 1.000

Non-American 9/23 = 0.391 l 14/23 = 0.609 l 23/23 = 1.000

Step-by-step explanation:

Give the exact value of the trigonometric function.

sec([tex]\frac{\pi }{2}[/tex])
A. 1
B. -1
C. 0
D. undefined

Please explain your answer, thank you! I'll give brainliest.

Answers

Answer:

D) undefined

Step-by-step explanation:

we would like to simplify the following

[tex] \displaystyle \sec \left( \frac{\pi}{2} \right) [/tex]

remember that, sec is the recipocal of cos

so,

[tex] \displaystyle \frac{1}{\cos \left( \frac{\pi}{2} \right) }[/tex]

by unit circle we acquire

[tex] \displaystyle \frac{1}{0}[/tex]

remember that, dividing by 0 is undefined

hence,

[tex] \displaystyle \sec \left( \frac{\pi}{2} \right) =\rm undefined [/tex]

please find the volume of the cone!!

Answers

[tex]volume = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]

Plugging in our values,

[tex]volume = \frac{1}{3} \times 3.142 \times {1}^{2} \times 2 = \frac{1}{3} \times 3.142 \times 2 = 2.095{m}^{3} \\ [/tex]

So the answer is,

[tex]2.095{m}^{3} [/tex]

The mean age of 5 women in an office is 23 years old. The mean age of 3 men in an office is 24 years old. What is the mean age (nearest year) of all the people in the office?

Answers

Answer:

23

Step-by-step explanation:

Women total age = 5 x 23 = 115

Men total age = 3 x 24 = 72

The mean age of all the people

= (115+72)÷(8)

= 23.375

= 23 (nearest year)

The mean age (nearest year) of all the people in the office is 23

How to determine the mean age?

The given parameters are:

5 women = 23 years

3 men = 24 years

Mean is calculated using:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{23 * 5 + 24 * 3}{5 + 3}[/tex]

Evaluate the quotient

[tex]\bar x = 23[/tex]

Hence, the mean age (nearest year) of all the people in the office is 23

Read more about mean at:

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solve for X. Assume that lines which appear tangent are tangent

Answers

Answer:

C

Step-by-step explanation:

Find the measure of the exterior angle.

Answers

Answer:

33+x+18=2x+3

51+x=2x+3

51-3=2x-x

48=x

Step-by-step explanation:

2x+3

2*48+3

96+3

99

What's the answer to

"find the value of
√121 + 3√125" "? ​

Answers

Answer:

11+15√5

Step-by-step explanation:

mat.hway

a book had a sale and it was 20% off. the price now is $7.00. What was the original price?





show work

Answers

Answer:

List Price = $ 8.75

Discount Amount = $ 1.75

the original price is $8.75 because 20% is 0.2 in decimal formation. multiply that to 8.75 and you get $1.75. if you subtract $1.75 from $8.75 you get $7.00

2. Nicholas has a pepper shaker in the shape of a cylinder. It has a radius of 9 mm and a height of 32 mm. How much pepper will fit in the shaker?

Answers

Answer:

sefsefff

Step-by-step explanation:

Writing a linear equations

Answers

Answer:

y = 1/2 x - 2

Step-by-step explanation:

The standard linear equationof a line is expressed as y = mx+b

Using the coordinate points (0, -2) and (2, -1)

Slope m = -1-(-2)/2-0

m = -1+2/2

m = 1/2

Since the line cuts the y axis sat y = -2, hence the intercept b = -2

Get the required equation;

Recall that y = mx+b

y = 1/2 x + (-2)

y = 1/2 x - 2

This give the required linear equation

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