In ΔJKL, k = 4.1 cm, j = 3.8 cm and ∠J=63°. Find all possible values of ∠K, to the nearest 10th of a degree.

Answers

Answer 1

Given:

In ΔJKL, k = 4.1 cm, j = 3.8 cm and ∠J=63°.

To find:

The value of  ∠K to the nearest 10th of a degree.

Solution:

According to the Law of Sine:

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

We have, In ΔJKL, k = 4.1 cm, j = 3.8 cm and ∠J=63°.

Using the Law of Sine, we get

[tex]\dfrac{j}{\sin J}=\dfrac{k}{\sin K}[/tex]

[tex]\dfrac{3.8}{\sin (63^\circ)}=\dfrac{4.1}{\sin K}[/tex]

[tex]3.8\sin K=4.1\sin (63^\circ)[/tex]

[tex]\sin K=\dfrac{4.1\sin (63^\circ)}{3.8}[/tex]

[tex]\sin K=0.961349[/tex]

[tex]K=\sin^{-1}(0.961349)[/tex]

[tex]K=74.0182[/tex]

[tex]K\approx 74.0[/tex]

Therefore, the measure of angle K is 74.0 degrees.


Related Questions

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5x+15293
There’s this app called Photomath and it helps with math:) have a great day

g(1)=0
g(n)=g(n-1)+n

g(2)=????

Answers

If g(1) = 0 and g(n) = g(n-1) + n, then g(2) = 2

The given relationship is:

g(1) = 0

g(n) = g(n-1) + n

g(2) = ?

Since g(1) is already known

g(2)  =   g(1)  +  2

Note that g(1) = 0

Substitute g(1) = 0 into g(2)  =   g(1)  +  2

g(2) = 0  +  2

g(2)  =  2

Therefore, if g(1) = 0 and g(n) = g(n-1) + n, then g(2) = 2

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Pls help
My teacher rlly tried to make it fun like girl nah it’s still hella boring

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Your saying you want all 5 of these questions answered?

How is the formula to find the slope between any two points the same as rise/run?

Answers

Answer:

because as long as it's the same number, the equation is still the same as long as you have the same numbers and you're using the same subtraction/addition properly

Step-by-step explanation:

If the legs of a right triangle are x, (2x - 1) and its hypotenuse is (2x + 1), what is the value of x?​

Answers

Answer:

x=8

Step-by-step explanation:

(2x + 1)² = x² + (2x - 1)² = x² + (2x - 1)(2x - 1)

(2x + 1)(2x + 1) = x² + 4x²-2x-2x+1

4x²+2x+2x+1 = 5x²-4x+1

4x²+4x+1 = 5x²-4x+1

0= 5x²-4x²-4x-4x+1-1

0= x²-8x

x²-8x=0

x²=8x

x=8

8 m (cubic meters) = dm3 (cubic decimeters)

Answers

Answer: 8000 dm³

Step-by-step explanation:

1 m³= 1000 dm³

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

Given

8 m³= dm³

Solve

8 m³ × 1000 dm³/m³=8000 dm³

Hope this helps!! :)

Please let me know if you have any questions

Two students were shopping for school supplies. They need spirals which cost x dollars and pens which cost y dollars. One student bought 2 spirals and 3 pens for $8.66. Another student bought 4 spirals and 5 pens for $15.20. Find the unit cost of a spiral.

Answers

Answer:

x=1.15

y=2.12

Step-by-step explanation:

look at the picture ..........

If 9x + 10=y what is y??

Answers

Answer:

above beat me to it he is right

Barry bought a wooden board that measured 8 feet in length. He cut off a piece that measured
6 5/9 feet. How much of the board was left?

Answers

B. is the answer i did the test and it was right

please answer both of these and show or tell me all your work

Answers

Answer:

5. 1:6 2/5

6. 1:5

Step-by-step explanation:

5. each time in the table you multiply H by 6 2/5 ex.

column 4 , 100x6=600, 2/5 of 100 = 40 and the total is 640, so the contant of proprtionality is 6 2/5

6. in the table there is a point on 2:10 and can be simplified to 1:5 so for every minute 5 gallons of water will be used

hope this helps sorry if this inst what your looking for have a blessed day :)

A construction crew is building a two story house, but they have not built the staircase between the floor yet. The height of the staircase is 12 feet, the base of the stairs will be 6 feet from the wall. How long does the temporary ramp need to be to the nearest tenth of a foot?

Answers

Answer:

13.4feet

Step-by-step explanation:

The set up forms a right triangle.

Given

Height of the staircase h = 12 feet

Base of the stairs b = 6feet

Required

Length of the ramp l

Using the pythagoras theorem

l² = h² + b²

l² = 12²+6²

l² = 144 + 36

l² = 180

l = √180

l = 13.42 feet

Hence the length of the ramp to the nearest tenth is 13.4feet

How do you find the x intercept and y intercept on a graph and when given an equation?

Answers

Answer:

In a graph, the x-intercept will be the point in which the line crosses the horizontal line of the plane.

The y-intercept is found when the line crosses the vertical line of the plane.

In an equation, y = mx + b, the y-intercept is the value of b, and the x-intercept is shown when y = 0. (substitute y for 0 and find the value of x)

Adam has 3 coins in his pocket and they are all different from each other. Ben has 3 coins in his pocket and they are all the same as each other. Adam has half as much money as Ben.
What are the coins they each have?

Answers

Answer:

The possible coins are:

P = penny = $0.01

N = nickel = $0.05

D = dime = $0.10

Q = quarter = $0.25

H = half dollar = $0.50

We know that Adam has 3 coins in his pocket, and all of them are different, then the money that Adam has can be represented with (A + B + C)

Behn has 3 coins, and all of them are the same, then if his coin has a value X, he has a total of 3*X

We know that Adam has half as much money as Ben, this can be written as:

(A + B + C) = 3*X/2

The easier way to solve this, is to play with different values of X, and see if we can find the values of A, B and C.

For example, if X = $0.10

then:

(A + B + C) = $0.10*(3/2) = $0.15

We can find 3 different value of coins for this equation? No, we cant, so X = $0.10 is also discarded.

if x = $0.50 then:

(A + B + C) = (3/2)*$0.50 = $0.75

Here we could have:

A = $0.50

B = $0.25

then: A + B = $0.75

But we still have the coin C.

If we take X = $0.25 then:

(A + B + C) = (3/2)*$0.25 = $0.375

We could round the right part to $0.40

then the coins in the left part would be:

A = $0.25

B = $0.10

C = $0.05

A + B + C =  $0.25 + $0.10 +  $0.05 = $0.40

This is a strech, but is the only thing we can make with the given problem.

Solve the inequalities by graphing. Select the correct graph. y> X y<-X​

Answers

Answer:

i think is y>X

Step-by-step explanation:

Hello!! I have a question, can you please answer it. ^^


The school nurse is assembling first-aid kits for the teachers. She has 75 bandages and 90 throat lozenges.
All the kits must have the same number of each supply, and all supplies must be used.

a. What is the largest number of kits the nurse can make?

b. How many bandages and lozenges will be in each kit?

Answers

Answer:

1. 75

2. 1

Step-by-step explanation:

(3/4) to the power of 2

Answers

Answer: 3/16

Step-by-step explanation: hope this helps :)

Answer:

0.5625

Step-by-step explanation:

Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,047
was collected on the sale of 1,291 tickets. How many of each type of ticket were sold?
The basketball game sold
adult tickets and
student tickets.

Answers

Answer:

The basketball game sold 439  adult tickets and  858 student tickets.

Step-by-step explanation:

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, in the systems of equations, one must look for the values ​​of the unknowns, with which when replacing, they must give the solution proposed in both equations.

Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,047  was collected on the sale of 1,291 tickets.

With "x" the number of adult tickets sold and "y" the number of student tickets sold, you have the following system of equations:

[tex]\left \{ {{x+y=1291} \atop {5*x+1*y=3047}} \right.[/tex]

Through the substitution method, you must solve for one of the unknowns in one of the equations and substitute its value in the following one: in this case you solve for the variable y from the first equation:

y=1291 -x

and you replace in the second equation:

5*x + 1291 - x= 3047

Solving, you get:

5*x-x= 3047 - 1291

4*x= 1756

x= 1756÷4

x=439

Replacing this value in the expresion y=1291 -x you get:

y=1291 -439

y= 858

The basketball game sold 439  adult tickets and  858 student tickets.

For a theater play, the school sold 120 blue tickets for students and 80 red tickets for adults. What percent of the tickets were sold to students?

Answers

Answer:

Step-by-step explanation:

120+80=200 the total number of tickets

120(student tickets) ÷ 200 (total tickets)= .6 =60%

Answer:

bin

Step-by-step explanation:

bghgghhshshsbabbsnajswjjegvrjrjrhrbrhrriritt

Points A, S, and R are ___.

Answers

Answer:

B

Step-by-step explanation:

I'm pretty sure it's B, (please let me know if I'm wrong.)  

Colinear means to be on the same straight line, which they are.  

Coplanar means to be in the same plane, which they appear to be as well.

So yeah I'm pretty sure it's B.  

-x+5+4x
simply the expression

Answers

Answer:

3x+5

Step-by-step explanation:

HELP FOLKS PLEASE ( i don't have much time)

Answers

Tan Angle y= 7/4
Tan Angle z= 4/7

Answer:

tan(Y) = 7/4

tan(Z) = 4/7

Step-by-step explanation:

Tangent ratios are the TOA of SOHCAHTOA.

tan( angle ) = opposite / adjacent

yo does anyone know how to solve this

Answers

(-7, 0)

i promise im right

x + 3 = 15
Solve the equation and check for the solution

Answers

Answer:

x=12

Step-by-step explanation:

move the 3 to the other side to get x by itself.

check: 12 + 3 = 15

Answer:

(Not sure)

x = 12

Step-by-step explanation:

x + 3 = 15

CLT

X = 15-3

× = 12

if we vibe for 3 hrs and become freinds how long will we be freinds?

Answers

Answer:

it depends

Step-by-step explanation:

I could be very committed,

im 15 in july my name is mercedes. and im bi, I skate and taken

I need help with this

Answers

A and C is the correct answers

Can you simply these fractions?

Answers

4/20 = 1/5

9/24 = 3/8

18/30 = 3/5

9/12 = 3/4

9/21 = 3/7

5/45 = 1/9

20/25 = 4/5

10/12 = 5/6

6/9 = 2/3

4/40 = 1/10

Explanation:

Find the greatest common factor then divide the numerator and denominator by the greatest common factor

Hope This Helps :)

4/20 = 4÷4 / 20÷4 = 1/5

9/24 = 9÷3 / 24÷3 = 2/8

18/30 = 18÷6 / 30÷6 = 3/5

9/12 = 9÷3 / 12÷3 = 3/4

9/21 = 9÷3 / 21÷3 = 3/7

5/45 = 5÷5 / 45÷5 = 1/9

20/25 = 20÷5 / 25÷5 = 4/5

10/12 = 10÷2 / 12÷2 = 5/6

6/9 = 6÷3 / 9÷3 = 2/3

4/40 = 4÷4 / 40÷4 = 1/10


Hope this helps!

Can some one please help me

Answers

Answer:

8:1

Step-by-step explanation:

Don reads 8 pages a minute. Therefore the amount of pages he could read is 8 and the amount of time it takes is a minute

What is 15/20 closest to 0,1/2 or 1

Answers

Answer:

0.07 (7/100) is closer to 0.

1.150 (1150/1000) is closer to 1.

0.391 (391/1000) is closer to 1/2.

0.0999 (999/10,000) is closer to 0.

0.99 (99/100) is closer to 1.

0.599 (599/1000) is closer to 1/2.

Put everything as a fraction. The first spot after the decimal means you put the number over 10, the second place means you put it over 100, the third 1,000, fourth 10,000 and so on. Hope I helped! ^^Step-by-step explanation:

The closeness of the given function is found to be by writing it in the simplest form as 1.

What is a fraction?

A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0.

The number a is called as the numerator and b is the denominator.

The given fraction is 15/20.

It can be simplified as below,

Divide numerator and denominator by the common factor 5 as,

(15 ÷ 5)/(20 ÷ 5)

⇒ 3/4

The given fraction 3/4 is greater than zero and closest to 1.

Hence, the given fraction is closest to integer 1.

To know more about fraction click on,

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Carlos and Lily want to know the combined amount of money they made last week. They both made $12 per hour, but Carlos also made a $35 bonus. Carlos says the combined amount is 12C + 35 + 120 where Cis the number of hours he worked, and L is the number of hours Lily worked. Lily says the combined amount is 12(C+ L) + 35. Who is right? Explain.

Answers

Answer:

Lily is right

Step-by-step explanation:

Carlos made:

12C + 35

Lily made:

12L

Together they made:

12C + 35 + 12L = 12(C + L) + 35

Lily is right. We don't know what 120 means in Carlos's equation, he should put 12L for Lily.

QRST is a parallelogram. Find x, y, and z.

Answers

Answer:

x=5.4

y= 9

z= 11

Step-by-step explanation:

5x= 27

x= 5.4

2y-5=y+4

y=9

3z = 33

z =11

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