A surveyor at point S locates a tree 200 meters away, at point T. The surveyor turns 120 degrees counterclockwise and locates a rock formation 150 meters away, at point R. Find the distance between the tree and the rock formation.

This will require using the law of cosines.

Answers

Answer 1

Answer:

190

Step-by-step explanation:

Answer 2

The distance between the tree and the rock formation is approximately 304.14 meters.

To find the distance between the tree (point T) and the rock formation (point R), we can use the law of cosines. The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's denote the unknown distance between the tree and the rock formation as 'd.'

We have a triangle with sides of lengths 200 meters (side ST), 150 meters (side SR), and d meters (side TR). The angle opposite side ST is 120 degrees.

According to the law of cosines:

d² = 200² + 150² - 2 * 200 * 150 * cos(120°)

Now, we can calculate this expression to find the value of d:

d² = 40000 + 22500 - 60000 * cos(120°)

Using the value of cos(120°) ≈ -0.5, we have:

d² = 40000 + 22500 - 60000 * (-0.5)

d² = 40000 + 22500 + 30000

d² = 92500

Taking the square root of both sides to solve for d:

d = √92500

d ≈ 304.14

Therefore, the distance between the tree and the rock formation is approximately 304.14 meters.

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Related Questions

I did this myself, but I kept getting negative numbers can someone else try and do this and see what you get ​

Answers

Answer:

6

Step-by-step explanation:

Answer:

67

Step-by-step explanation:

4x = 2x + 12

4x - 2x = 2x - 2x + 12

2x = 12

2x ÷ 2 = 12 ÷ 2

X = 6

Plug into HI

9 × 6 + 13 = 67

24x^2 + 26x - 104 solve for x

Answers

Answer: 24x2+26x−104 or -104

Step-by-step explanation:

if two sides of a triangle measurement 8cm 12cm what is the range of the third side

Answers

Umm I think maybe 4cm or 16cm

w is directly proportional to u if w=5 when u=3,find u when w is =2/7​

Answers

Answer:

u = 6/35

Step-by-step explanation:

w = k * u

w = ku

Where

k = constant of proportionality

if w=5 when u= 3

w = ku

5 = k * 3

5 = 3k

k = 5/3

find u when w is =2/7​

w = ku

2/7 = 5/3 * U

2/7 = 5/3u

u = 2/7 ÷ 5/3

= 2/7 × 3/5

= (2*3)/(7*5)

= 6/35

u = 6/35

Help me out plz ????

Answers

96 cm^2

Each side has an area of 24 cm^2, so just multiply that by 4

If AD=8 and BD=4, what is the length of DC⎯⎯⎯⎯⎯⎯?

The figure shows right triangle C A B with altitude A D to hypotenuse B C.

DC = 4
DC = 20
DC = 8
DC = 16

Answers

Answer:

the answer should be 16!

BRAINLIEST to wherever gets this correct ​

Answers

Answer:

[tex]300\pi[/tex] cubic feet

Step-by-step explanation:

Let r be the radius of cone and h be the height of cone.

Radius of cylinder=r

Height of cylinder=h

Volume of cone=[tex]100\pi ft^3[/tex]

We have to find the volume of cylinder.

We know that

Volume of cone=[tex]\frac{1}{3}\pi r^2 h[/tex]

[tex]100\pi=\frac{1}{3}\pi r^2 h[/tex]

[tex]r^2 h=300[/tex]

Volume of cylinder=[tex]\pi r^2 h[/tex]

Using the formula

Volume of cylinder=[tex]\pi (300)=300\pi ft^3[/tex]

Hence, the volume of cylinder=[tex]300\pi[/tex] cubic feet

a man sold two jeans at Rs 800. On one he gains a profit of 10 percent on other he loses 15 percent how he gain or loses in whole transaction

Answers

Answer:

1st jean:

100%-> 800

110%->880

880-800=80 ( earned)

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

2nd jean:

100%->800

85%->680

800-680=120(lost)

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

120-80=40 (lost)

can someone pls help me
write 3lgx + 2-lgy as a single logarithm​

Answers

Answer:

log(x^3*y^(-2))

Step-by-step explanation:

two log rules you need to know for this question:

alogb = log(a^b)

logx + logy = logxy

you can start by getting rid of the term in front of the log, or a

also is it 2 minus or 2 times negative? im assuming it's 2 times negative because it is more likely

log (x^3) + log (y^-2) = log (x^3*y^-2)

Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently.

Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300.


100 POINTS
Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn.

Salesman C does not earn any commission. His weekly salary is $900.
The weekly paycheck amount for each salesman, p, is a function of the number of sales, s, they had in that week.

Answers

Answer:

Equations for each salesman:

A. p(s) = 65sB. p(s) = 40s + 300C. p(s) = 900

When s = 0, s= 1, s = 10 each of the gets paid:

A. p(0) = 0, p(1) = 65, p(10) = 650B. p(0) = 300, p(1) = 340, p(10) = 700C. p(0) = p(1) = p(10) = 900

The above numbers as ordered pairs:

                 A                B               C          s = 0  |    (0, 0)       | (0, 300)    | (0, 900)s = 1   |    (1, 65)      | (1, 340)     | (1, 900)s = 10 |    (10, 650) | (10, 700)   | (10, 900)

Aubrey's dinner cost $85 She tips the waitstaff 30%, percent for excellent service.

Answers

Answer:

She tipped $25.50 and paid a total of $110.50

Step-by-step explanation:

hope this helps you out

A jogger is running with an initial speed of 5 m/s. The jogger then sprints to the finish line, increasing their speed to 10 m/s over 5 seconds. What is the jogger's acceleration in m/s squared?

Answers

Answer:

Step-by-step explanation:

1 m/s square

A shirt costs $5 less than a sweater. Together they cost
$25. How much does the sweater cost? _____

Answers

Answer:

$20

Step-by-step explanation:

25-5=20 that is your answer

Answer:

15 dollars

Step-by-step explanation:

Select the correct answer.
Steven went to play video games in Games Galore arcade. Games Galore charges $1.50
for each game played. Represent the relationship between total cost, y, and number of
games played, x using a table, graph and equation. Is this relationship a proportional or
additive relationship? Explain.
Proportional
Additive

Answers

Answer:

The answer is proportional

Step-by-step explanation:

I took the test and got 5/5

The given relationship is a proportional relation.

What is proportionality?

In mathematics, proportionality indicates that two quantities or variables are related linearly. If one quantity doubles in size, so does the other; if one of the variables diminishes to 1/10 of its former value, so does the other.

Given that, Steven went to play video games in Games Galore arcade. Games Galore charges $1.50 for each game played

Establishing the equation, we get,

y = 1.50x

Where 1.50 is the slope of the line, and, y is total cost and x is the number of game played.

When x = 2,

y = 1.50X2

y = 3

(2, 3)

When x = 4

y = 1.5X4

y = 6

(4, 6)

When x = 6

y = 1.5X6

y = 9

(6, 9)

Here we see that the value of y is varying from the value of x by 1.5 times.

Hence, The relation is a proportional relation.

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8r2 in fraction form

Answers

8r^2 eight r squared hope this is right

It is the simplest fraction form

Ethan is designing a new board game, and is trying to figure out all the possible
outcomes. How many different possible outcomes are there if he spins a spinner with
three equal-sized sections labeled Walk, Run, Stop and rolls a fair die in the shape of
a cube that has six sides labeled 1 to 6?

Answers

Answer:

18

Step-by-step explanation:

3x6

You deposit $250 in an account. The account earns $20 simple interest in 4 years. What is the annual interest rate?

Answers

Answer:

5.00

Step-by-step explanation:

20/4 years = 5 per year

helpppppppppppppppppppppppppppppppp plzzzzzzzzzzzzzzzzzzzz

Answers

Last one I got 5 37/45 but it says round to the nearest

Pensé dos números. Sumados dan 38 y restados dan 2. ¿Qué números son?

Answers

Answer:

sorry I cannot help you sir can you translate it into English

I need help on this assignment, I need to find the angles of the blank spaces. Anything is appreciated!

Answers

Answer:

3: 97

10: 97

9: 83

5: 97

7: 83

16: 97

Im 100% on these answers bc Ive already taken this class :)

Answer:

Step-by-step explanation:

9) m∠3 = m∠2  {Vertically opposite angles}

m∠3 = 97

m∠10 = m∠2       {Corresponding angle}

m∠10 = 97

m∠9 +m∠10 = 180  {Linear pair}

m∠9 + 97   = 180

         m∠9 = 180 - 97

        m∠9  = 83

m∠6 = 83

m∠5 + m∠6 = 180 {linear pair}

m∠5 + 83 = 180

         m∠5 = 180 - 83

m∠5 = 97

m∠7 = m∠6  

m∠7 = 83

m∠8 = m∠5           {Vertically opposite angles}

m∠8 = 97

m∠16 = m∠8      {Corresponding angle}

m∠16 = 97

Pete is choosing his clothes for the day. His bottoms will be either cargo shorts(C) or jeans (J). His top will be T shirt (T), sweatshirt (S), or long sleeved shirt (L)

Answers

The question is incomplete. Here is the complete question.

Pete is choosing his clothes for the day. His bottoms will be either cago shorts (C) or jeans (J). His top will be T-shirt (T), sweatshirt (S) or long sleeved shirt (L).

Which is a complete list of the possilbe outfits he can choose from?

CT, CS, CL, JT, JS, JL

CJ, CT, CS, CL

CJT, CJS, CJL

CT, TC, JS, SJ, CL, LC

Answer: CT, CS, CL, JT, JS, JL

Step-by-step explanation: The Fundamental Counting Principle is a method of determining a number of ways independents events can occur, i.e., it states that if there are t ways of doing something and w ways of doing another, then there are t x w ways of doing both things.

For example:

Peter has 2 choices of bottom and 3 choices of top. So, according to the principle, he will have 2 x 3 choices of clothing.

And the choices are:

shorts and t-shirt = CT

shorts and sweatshirt = CS

shorts and long sleeved = CL

jeans and T-short = JT

jeans and sweatshirt = JS

jeans and long sleeved = JL

The order he chooses doesn't matter.

So, the right alternative is CT, CS, CL, JT, JS, JL.

Is -50 greater than 2

True or false

Answers

FALSE

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

because negative (-) numbers are always smaller than positive (+) numbers

2x+3y=1470 changed to slope intercept form, write a description which is clear precise and correct of how to graph the line using the slope intercept method,changes equation to to function notation and explains clearly what the graph of the equation represents. graph the equation and labels the intercept correctly. Write at least 3 sentences explaining how the graphs of the two equations are the same and how they are different.

Answers

Answer:

y= 490 - 2x

Step-by-step explanation:

Answer: Do I get brainliest if I try? 7 = 490 - 2x

Step-by-step explanation:

The figure shows two lines cut by transversal.wich statement correctly explains why the two lines are parallel

Answers

Answer:

D

Step-by-step explanation:

This is because the angle are corresponding which mean they are on the same side and are the same number

Hope this Helped

Plz help due tomorrow

Answers

Answer:

 It's C) -6y

Step-by-step explanation:

I know someone already answered but I figured I could explain since it looks like you are getting a little confused. The reason it's not A is because its

-5 + 5 which is zero. So it gets rid of x so your just left with -6y. If it was

5x+5x then it would 10x but the negative makes it 0

Can someone help me please?

Answers

3/10=0.3=30%

725/1000=0.725=72.5%

4/10=0.4=40%

Mori is building a cage for his pet guinea pig. The bottom is 8 inches
long and 8 inches wide. How big is the bottom of the cage?

Answers

[tex]area = lw[/tex]

[tex]area = (8)(8)[/tex]

[tex]area = 64 \: {inches}^{2} [/tex]

//

[tex]perimeter = 2(l) + 2(w)[/tex]

[tex]perimeter = 2(8) + 2(8)[/tex]

[tex]perimeter = 32 \: inches[/tex]

please help me with this

Answers

Answer: A. 2[tex]\sqrt[3]{6}[/tex]

Step-by-step explanation:

The side lengths of a triangle are 9, 12, and 18. Is this a right triangle? O A. Yes, because 92 + 122 ​

Answers

Answer:

O A. Yes, because 92 + 122 = 152

B. No, because 9 + 12 15.

C. Yes, because 92 + 122> 152.

D. No, because 92 + 122 + 15 ^2

1

SEE ANSWER

Step-by-step explanation:

What is 3 3/4 - 2 1/3

Answers

Answer:

1 5/12

Step-by-step explanation:

decimal form, 1.416

Answer:

3 1/4 + 2 1/3 = 67/

12

= 5 7/

12

≅ 5.5833333

Step-by-step explanation:

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