In math class, James, Hadley, and Gwen were challenged to go stand on the field in a random location and find the distance between themselves using only one length. They were also each given a protractor to find the angle between each other. Using this diagram, solve for the missing side lengths of the triangle. Round to the nearest hundredth. A triangle where James, Hadley, and Gwen are labelled on the vertices. The angle of James is 61 degrees, Hadley is 73 degrees, and Gwen is 46 degrees. The one length that is labelled is between James and Hadley and measures at 15 meters. Gwen to Hadley is what? Gwen to James is what?

Answers

Answer 1

The interior angles of the triangle of 61°, 73°, and 46°, and the distance from James to Hadley of 15 meters gives;

Gwen to Hadley ≈ 18.24 meters

Gwen to James ≈ 19.94 meters

How can the distances between the students be found?

The given angles are;

At James's location; 61°

At Hadley's location; 73°

At Gwen's location; 46°

The distance between James and Hadley = 15 meters

The angle facing the distance between James and Hadley is the angle at Gwen, 46°

The angle facing the distance between Gwen and James is the angle at Hadley, 73°

The angle facing the distance between Gwen and Hadley is the angle at James, 61°

The angle that faces the 15 meter length is the angle at Gwen, which is 46°

By the rule of sines, the distance from Gwen to Hadley is therefore;

[tex] \frac{15}{sin( 46 ^ \circ)} = \frac{Gwen \: to \: Hadley}{sin( 61 ^ \circ)} [/tex]

Which gives;

[tex] Gwen \: to \: Hadley= \frac{15 \times sin( 61 ^ \circ) }{sin( 46 ^ \circ)} \approx 18.24[/tex]

Gwen to Hadley ≈ 18.24 meters

Similarly, we have;

[tex] \frac{15}{sin( 46 ^ \circ} = \frac{Gwen \: to \: James}{sin( 73 ^ \circ)} [/tex]

Therefore;

[tex] Gwen \: to \: James = \frac{15 \times sin( 73 ^ \circ) }{sin(46 ^ \circ)} \approx 19.94 [/tex]

Gwen to James ≈ 19.94 meters

Learn more about the rule of sines here:

https://brainly.com/question/4372174

#SPJ1


Related Questions

A. 2 sqrt 3

B. 4

C. 8

D. 4 sqrt 6

E. 12


Please help

Answers

Answer:

Option B. 4

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle θ = 60 °

Opposite (Fe) = 4√3

Adjacent (DE) = x

The value of x can be obtained by using the Tan ratio as illustrated below:

Tan θ = Opposite / Adjacent

Tan 60 = 4√3 / x

√3 = 4√3 / x

Cross multiply

√3 × x = 4√3

Divide both side by √3

x = 4√3 /√3

x = 4

Thus, the length of DE is 4

If sin 0 >0 and cos 0 = 0, then which of the following is
true?

Answers

Answer:

Step-by-step explanation:

There's no list but one answer would be sin O = 1.

A train travels 150 km in the same time that a plane covers 525 km. If the speed of the plane is 20 km per hr less than 4 times
the speed of the train, find both speeds.

Answers

Answer:

Step-by-step explanation:

simplify:
(5x-4)+(3-4x)

Answers

Answer:

x - 1

Step-by-step explanation:

combine like terms

(5x -4x) = x

(-4 + 3) = - 1

Answer:

x - 1

Step-by-step explanation:

(5x - 4) + (3 - 4x)

5x - 4 + 3 - 4x

-4x          -4x

x - 4 + 3

x - 1

Zoo tickets cost seven dollars a person if the zoo brought in 1302 on Friday how many people visited that

Answers

Answer:

the awnser would be. 1302÷7=186

Step-by-step explanation:

you divide.

Answer: 186 people

1302 ÷ 7 = 186

EFG, e = 9.8 cm, f = 3 cm and ∠G=167°. Find the length of g, to the nearest 10th of a centimeter.

Answers

Answer:

Step-by-step explanation:

Answer:12.7

Step-by-step explanation:

Which figure is a pyramid? A cone. B cylinder. C rectangular prism. D pyramid.

Answers

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Solve the equation 2x + 4 - 9 Explain the steps
and properties you used.

Answers

Answer:

2x - 5

Step-by-step explanation:

2x + 4 - 9

the 2x gonna stay

so you take 4 - 9 = -5

so the answers gonna be 2x - 5

bc the 5 is negative so you gonna subtract

I hope you understand my english...

HELP PLSSSSSSSSSSSSSSSSSSSSSSSSS

Answers

C , I took a guess so if it’s wrong sorry

what is the place value of 3 in 553 049 270?​

Answers

Answer:

1 million

Step-by-step explanation:

Start counting at position 0, the rightmost position has value 10⁰ = 1

The one left to that 10¹ = 10

... and so forth ...

The 6th position has value 10⁶ = 1000000, a.k.a. one million.

The place value of 3 in 553 049 270 is 1 million.

Here the number is given as 553 049 270.

We have to find the place value of 3 in given number.

What is Place value?

Place value is describe the position or place of a digit in a number.

Now,

To find the place value of 3;

Start counting at position 0, the rightmost position has value [tex]10^{0}= 1[/tex]

The position of 7, one left to 0, has value [tex]10^{1} = 10[/tex]

------ and so on.

Now, position of 3 is 6th position has value [tex]10^{6} = 1000000[/tex]

So, The place value of 3 in 553 049 270 is 1 million.

Learn more about Place value visit:

https://brainly.in/question/16613482

#SPJ6

Find the value of x. I WILL GIVE 60!!! POINTS ANSWER QUICK!

Answers

Answer:

120 degrees

Step-by-step explanation:

Rsm right?

I NEED HELP ASAP how do you solve -2x(3y +9) in the distributive property pls thank you

Answers

Answer:

-6xy-18x

Step-by-step explanation:

To solve -2x(3y+9), multiply -2x by 3y and 9.

-2x(3y)+-2x(9)

Solve

-6xy-18x

Answer:

-24 i think

Step-by-step explanation:

Is xy= 60 a direct variation or inverse variation

Answers

Answer:

Inverse variation

Step-by-step explanation:

Direct variation:

[tex]\dfrac{y}{x}=constant[/tex]

Inverse variation:

[tex]xy=constant[/tex]

We have

[tex]xy=60[/tex]

it's an inverse variation.

find the value of each variable using sine and cosine. round your answers to the nearest tenth​

Answers

Answer:

x=9.5 and y=15.3

Step-by-step explanation:

to find x you do sine of 32 = x/18 because the sine is opposite/hypotenuse

you put in a calculator sine (32) x 18 and get 9.538546756

so x equals 9.538546756 but it says to round to the nearest tenth so x equals 9.5

to find y you do the cosine of 32 = y/18 because cosine is adjacent/hypotenuse

cosine of (32) x 18 = 15.26486573 so you equals 15.26486573 but since you have to round to the nearest tenth y = 15.3

The value of x is 9.54.

The value of y is 15.3.

What are trigonometric identities?

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

From the figure,

Sin 32 = x / 18

Cos 32 = y / 18

Now,

Sin 32 = 0.53

Cos 32 = 0.85

Now,

0.53 = x / 18

Multiply 18 on both sides.

x = 0.53 x 18

x = 9.54

0.85 = y / 18

Multiply 18 on both sides.

y = 0.85 x 18

y = 15.3

Thus,

The value of x is 9.54.

The value of y is 15.3.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ2

10. A rectangle has a perimeter of 22 cm. If the length of the rectangle is 2 cm more than two times the
width, what are its dimensions?

Answers

Answer:

w = 3 cm

l = 8 cm

Step-by-step explanation:

let 'w' = width

let '2 + 2w' = length

P = 2l + 2w

22 = 2(2 + 2w) + 2w

22 = 4 + 4w + 2w

22 = 4 = 6w

18 = 6w

w = 3

length = 2 + 2(3) = 18

Desmond went to a concert with his three other friends and he decided to pay for the tickets and his friends would pay him back. The total of the tickets was $108. Write and solve an equation that will find how much it is for one ticket.

Answers

I would say 108 divided by 4 = 27 but I may be wrong

A table is 2 feet wide. It is 6 times as long as it is wide.

Answers

Answer:

The table is 12 feet in length

Step-by-step explanation:

2 * 6 = 12

12 feet in length

The area of a rectangle is given as:

Area = Length x width

The perimeter of a rectangle is given as:

Perimeter = 2 (length + width)

The area of the table is 24 square feet.

The perimeter of the table is 28 feet.

What is a rectangle?

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

The perimeter of a rectangle is given as:

Perimeter = 2 (length + width)

We have,

Table:

Width = 2 feet

Length = 6 x 2 feet = 12 feet

We will assume that the table is a rectangle.

The area of the table:

= Length x width

= 12 x 2

= 24 square feet.

The perimeter of the table:

= 2 (length + width)

= 2 (12 + 2)

= 2 x 14

= 28 feet

Thus,

The area of the table is 24 square feet.

The perimeter of the table is 28 feet.

Learn more about rectangles here:

https://brainly.com/question/15019502

#SPJ2

will give brainliest IF CORRECT

What is the name of the angle
relationship?

vertical angles
supplementary angles
complementary angles

Answers

Answer:

They are supplementary angles.

Hope it will help :)

8 slices of pizza and 5 sodas cost $36.50. 4 Slices of pizza and 10 sodas cost $37. How much does a slice of pizza cost? How much does a soda cost?


PLEASE HELP

Answers

Step-by-step explanation: If we use the variable p to represent our pizzas and s to represent our sodas, if our first equation states than 8 slices of pizza and 5 sodas cost $36.50, that's 8p + 5s = 3650.

Notice that I expressed cost in terms of cents so

that we can avoid having to deal with decimals.

In our second equation, 4 slices of pizza and

10 sodas cost $37, that's 4p + 10s = 3700.

Now let's rewrite our two equations on top of one another.

8p + 5s = 3650

4p + 10s = 3700

To solve this system of equations, I would use addition.

I would multiply the bottom equation by -2

to create a situation where our p's will cancel.

When we do that, we get -8p - 20s = -7400.

Now rewrite the equations once again ~

8p + 5s = 3650

-8p - 20s = -7400

Now add the equations together.

So we have -15s = -3,750.

Divide both sides by -15 and s = 250.

Remember that I expressed cost in terms of cents so

since s = 250, it really means that a soda is $2.50.

Now just plug an s back in for the s in one equation.

When we do this, we find that p = 300.

So a pizza is $3.00

Please help pleasseee

Answers

Step-by-step explanation:

hope this is correct.......

Answer:

M = 26

Step-by-step explanation:

4m + 3m - 5 + 3 = 180 degree

7m -2 = 180 degree

7m = 180+2

7m = 182

m = 182/7

m =   26

26 x 4 - 5 = 104 - 5 = 99

26 x 3 +3 = 78+ 3 = 81

8. what is the volume of these 5 objects

Answers

Answer:

1) B

Step-by-step explanation:

To get the volume of a cube, you multiply the length, width and height together. 4 x 7 x 8 = 224. 8 × 5 × 6 = 240. This means that chocolate box B has the larger volume.

multiples that are shared by two or more numbers called

Answers

Answer: Common Multiples

Step-by-step explanation:

There are four primary strategies for determining the area of two-dimensional figures and shapes: a) counting square units, b) subdividing the shape into pieces, finding the areas of the pieces and adding the areas together, c) enclosing the shape in a rectangle, finding the area outside of the shape but inside the rectangle and subtracting, and d) using a formula. Explain each strategy. Use an example for each.

Answers

Answer:

Given below

Step-by-step explanation:

a) if we look at the picture then we can find by counting the square units. In each box there are 3.5 square units along the breadth. There are 3 square units along the length . Counting these gives (3*3.5= 10.5 ) 10.5 square units for each box. Adding the 10.5 +10.5+10.5+10.5 = 42 square units gives the area of the inner rectangle.

b) There are 4 boxes and the total area of the these boxes will be 4*10.5= 42 square units.

Area of 1 box = 3*3.5= 10.5

c)  The area of the outer rectangle = 8*12= 96 square units.

The area between the two rectangles along the breadth = 3*7= 21 of one side.

The area between the two  sides along the length = 6*1= 6 square units.

Subtracting 21+21+6+6= 54  from 96 gives  42 square units

d)  Area= length *breadth

           = 6* 7= 42 square units.

Hence by all four methods the total area remains the same.


I need help with this

Answers

Answer:

I believe D

It's sheds video games in a good light!

Hope that helps!

Answer:

yeah d seems to be the most likly

Step-by-step explanation:

it’s MATH who knows how to do this i’m down bad

Answers

Answer/Step-by-step explanation:

1. 7x + 2 = 5x + 22 (alternate interior angles are congruent)

Collect like terms

7x - 5x = -2 + 22

2x = 20

2x/2 = 20/2

x = 10

2. 13x - 6 = 10x + 24 (alternate interior angles are congruent)

Collect like terms

13x - 10x = 6 + 24

3x = 30

3x/3 = 30/3

x = 10

3. (12x + 26)° + 46° = 180° (same side interior angles are supplementary)

12x + 26 + 46 = 180

12x + 72 = 180

12x + 72 - 72 = 180 - 72

12x = 108

12x/12 = 108/12

x = 9

4. (5x + 5)° + 135° = 180° (same side interior angles are supplementary)

5x + 5 + 135 = 180

5x + 140 = 180

5x + 140 - 140 = 180 - 140

5x = 40

5x/5 = 40/5

x = 8

Kristy ran a mile in 6.58 minutes. She ran her second mile in 7.15 minutes. What was the time difference between her first and second mile.

Answers

Answer:

17 seconds

Step-by-step explanation:

7.15 minus 6.58 is .17 or 17 seconds

Answer:

17 seconds

Step-by-step explanation:

7 minutes and 15 seconds minus 6 minutes and 58 seconds

You also have to remember that in a minute, there is 60 seconds, not 100

solve the two step equation and identify the steps
2= - 7/4 + 1/4 x

Answers

Answer:

What you need to do is to solve. 2 = -7/4 + 1/4 x

You can try to have same denominator in all numbers to be able to multiply the right and left side by it and remove it

We can write it like this:

8/4 = -7/4 + 1/4  x

We multiply by four the two sides  and get

8 = -7 + x

We can sum 7 to both sides

8 + 7 = x

x= 15

We can replace to see if it's correct

-7/4 + 1/4 * 15 = -7/4 + 15/4 = 8/4

Is 1/3 less than or greater than 5?

Answers

Answer:

Less than

Step-by-step explanation:

not a whole #

A total of 560 tickets were sold
They were either adult or Student
tickets.
The number of Student tickets
Sold was 3 times the number of
adult tickets. How many adult
tickets sold

Answers

Answer:

Student.... 420

Adult.......140

Find the length of the missing side.
13
B
A
5
A) 13.9
B
7.
© 11
D) 12
E Not enough information.

Answers

Answer:

D

Step-by-step explanation:

12 cm,

Simply use Pythagora's theorem. The square of the hypotenuse = the sum of the squares of the other two sides

So, you get the square of the missing side by subtracting 5 squared from 13 squared, which gives 144.

Square root of 144 is the length of the missing side, i.e. 12 cm.

Other Questions
A and B are independent events. P(A) = 0.60 and P(B) = 0.30.What is P(A and B)?A. 0B. 0.18C. 0.90D. 0.018 True or false: Personality tests tend to be the best and most useful way to assess someone's personality due to its objectivity and lower potential for bias/human error. From the perspective of mertons strain theory of deviance, a mugger and a stock broker are similar in that both:______. What Christian belief does Donne express in the last two lines? hich of the following conditions is characteristic of a monopolistically competitive firm in both the short run and the long run A device known as ___________________________________ is deployed in an occluded coronary artery to restore the blood flow to the wall of the heart. What is the correct order for structures in the nervous system pathway for hearing? a. axons project to the auditory cortex. b. axons project to inferior colliculi. meaning of clothing Consider the equation x+4=2x+19. Let f(x)=x+4and g(x)=2x+19. The graph of each function is shown. Coordinate plane with the graphs of two lines. The horizontal x axis labeled from negative three to nine in increments of one. The vertical y axis labeled from negative two to nineteen. The line f of x passes through ordered pairs zero comma four and two comma six. The line g of x passes through the ordered pairs zero comma nineteen and one comma seventeen. At what point do the graphs intersect? Enter your answer in the box. Why is it important for you, the first aid responder, to ask questions using SAM and do a focused check of the responsive person |||Read the passage.3.04 Unit Test: Viewpoint and PurposeA Complication or TwoThe rejection letter from my Ivy League school of choice was thefirst major obstacle I encountered in my grand 10-year plan. Itwas not the last. I was 17, and at the time quite certain thatnothing would derail me from my grandiose future. I planned toachieve everything my parents expected, and more. The firststep was supposed to have been attending my parents' almamater, graduating with honors, and then moving on to law schoolwithout pausing to let my peers-or competitors-catch me. Tosay that's not how it went is a gross understatementNeeding a distraction in my moment of crisis, I decided to pickup another couple of hours of volunteer service. I rode thesubway to Tri-Valley Hospital with that rejection letter wrinkled inmy right fist. I probably should have left it at home, but I couldn'tbring myself to put it down. I'd spent so many hours volunteeringat To Wallace to hold mPhasiand that the AWhat is the author's purpose for writing this text?O to encourage young people to create a life planO to share something he has learned about lifeOto tell an amusing story about how he met his wifeOto argue that medicine is a better career than law Which of the following is 25 9/16 equal to? Rewrite each sentence using the appropriate form of "ser" and the correct stressed possessive pronoun.Model:- Los pantalones son de Pepe.- Son suyos.1. La falda es de Julia.2. Los impermeables son de ustedes.3. Son tus medias.4. La cartera es de nosostros.5. Son mis pantalones cortos. Calculate the following ratios, correct to 3 decimal places. a. sin 58 = b. cos 26 = c. tan 63=. Animals that lie in cold climates tend to have higher proportions of __________ fatty acid residues in their lipids than do animals that live in warm climates. were Japanese American minorities treated fairly or unfairly during world war II? Saving is always equal to:_______ Q.2. If the line y=x is reflected over the x - axis and made flatter(less steep) by a factor of then write the equation of the new line Examine the inequality and its graph. Which values are part of the solution set? Check all that apply. x = 3 x = 5 x = negative one-half x = 4.5 x = 4 What compromises were required to pass health care reform in March 2010? How might those compromises have affected public perception of the bill?