In Triangle DEF, f = 160 cm, d = 670 cm and ZE=114°. Find the length of e, to the nearest
centimeter.

Answers

Answer 1

Answer:

This is an obtuse scalene triangle with the length of E measuring around 749 cm.

<D = 54.754° ≈ 55°

<E = 114°

<F = 11.246° ≈ 11°

Side D = 670 cm

Side E = 749.46937 cm ≈ 749 cm

Side F = 160 cm

Explanation:

When given two sides, and an angle, we can use trigonometry to find the missing angles, and sides.

Given the triangle ∆DEF with side D measuring 670 cm, side F measuring 160 cm, and angle E measuring 117°, we can apply the law of sines to identify the missing information. A & a chronologically refers to the first angle, and side. B & b chronologically refers to the second angle, and side. And C & c chronologically refers to the third angle, and side.

a / Sin (A) = b / Sin (B) = c / Sin (C)

[side 1]. [side 2]. [side 3].

↓ ↓ ↓

sideD/sin(<D) SideE/sin(<E) SideF/sin(<F)

______________________________

670cm / Sin(D) = E cm / Sin(114) = 160 / sin(F).

Since we are only given two sides with an angle measure, we can refer to the law of cosines to figure this one out.

It states that A = arccos(b²+c²-a²/2bc) → cos(A) = b²+c²-a²/2bc

B = arccos(a²+c²-b²/2ac) → cos(B) = a²+c²-b²/2ac

and C = arccos(a²+b²-c²/2ab) → cos(C) = a²+b²-c²/2ab

capital A, B, and C are angles A, B, and C.

lowercase a, b, and c are sides a, b, and c.

Therefore c² = a² + b² − 2ab cos(C),

b² = a² + c² - 2ac cos (B), and a² = b²+c² - 2bc.

SOH CAH TOA.

Since we know this, we can solve for pretty much everything as long as we are given at least 3 variables. Chronologically, because we are solving for side e, we must use b² = a² + c² - 2ac cos (B), because the rest are only variables we are given, making it easy to solve. So b² = 670² + 160² - 2(670 × 160) × cos(114°) = 561704.3362754.

Now take the square root of that to get b by itself, so √561704.3362754.... = 749.4693698046.... ≈ 749

Answer 2

Answer:749

Step-by-step explanation:

S.A.S law or Cosines

e=561704.33628= 749.469= 749


Related Questions

Lines m and n are parallel 70° a с d n Find the missing angle measures Enter your answers in the boxes ​

Answers

A is 110, B is 70, C is 110, D is 70, G is 110, E is 110, and F is 70

Find the area of a square with side length x when x is equal to the given value.
Are the area of a square and the length of its side directly proportional? Justify
your answer.
x = 10 in.

Answers

Answer:100

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Because you multiply 10 * 10.  Which equals 100.  And they are not directly proportional quantities.

The Wells family goes out to eat dinner every Saturday night. Last Saturday was the 100th time the family had eaten at Happy Joe's Pizza House. The owner of Happy Joe's gave the family a 20% discount for customer loyalty. The bill was $27.50 before the discount. What was their bill after the discount?

Answers

33 dollars because 27.50 times .20 is equal to 5.5 so you add 27.50 plus 5.5 equal to 33 dollars

whats 2+2 very hard I know

Answers

Answer:

4

Step-by-step explanation:

Answer:

2+2= 4

is very hard I know

THANKS

guys please help!!!! i NEED to get these right to pass!!!! I WILL GIVE THE BRAINLIEST!!!!

Answers

Answer:

Answer in order, 12,14, (4,3), x2, 4, 12, 3

Step-by-step explanation:

PLEASE MARK BRAINLIEST

Evaluate 8(6+5)/2²+6(2)​

Answers

Answer:

34

Step-by-step explanation:

1. Add 6 and 5 and that multiplies with 8 which would be 88

2. Then divide by 4, leaving you with 22.

3. Add that with 6(2), 12, and that gives you 34

Use Pemdas. 6+5 = 11 . then 2 to the 2nd power is 4. 8x11 =88 then 6x2 is 12 .. 88 divided by 4 is 22 . Last 22+12 is 34.

can someone please help.....​

Answers

1/3 is smaller than 1/2, therefore it already indicates the number line is drawn incorrectly, since 1/2 should be in front of 1/3 not behind & 1/12 should be in front, next to 0, since it is the smallest fraction and 1/6 right next to it, then 1/3, then 1/2 & 5/12 then 1/4.

Ricardo bought 3 pounds of gummy bears for $7.77. What is price per pound for the gummy bears?

Answers

Answer: To find the price per pound we must divide 7.77 by 3, 7.77/3=2.59. So the price per pound for the gummy bears is 2.59$.

Answer:

2.59

Step-by-step explanation:

James runs 8 laps in 14 minutes. How many laps can he run in one hour and ten minutes?

Answers

Answer: Don't come at me if I'm wrong, but I believe it's 40 laps.

Step-by-step explanation:

First, you need to figure out how many laps James runs in 1 minute and you can do this by dividing the number of laps and minutes (8 laps/14 minutes). This should give you 4/7 laps/minute.

Next, you figure out how many minutes 1 hour and 10 minutes is (just to make things easier) 1 hour and 10 minutes = 70 minutes

Then, you multiple 4/7 and 70 and you get 40 laps.

Answer:

40 laps

Step-by-step explanation:

I just put this into a proportion

so basically i just did 8/14 = ?/70

Then i just worked it like any other problem

8 x 70 then divide 14 and i got 40.

so James ran 40 laps in one hour and tens minutes

NOTE that i turned one hour and ten minutes into minutes

pls mark brainleist

hii i need help on another question!
find the total cost to the nearest cent.
$24 shirt; 6% tax

Answers

The answer is $25.44. You need to add the cost of the shirt and the tax together for the answer. The cost of the shirt is $24 and the tax of it is $1.44. So $24 + $1.44 = $25.44.

Answer:

$25.44

Step-by-step explanation:

total cost of shirt = $24 x 1.06

                            = $25.44

Find the unit rate. Round to the nearest hundredth, if necessary.

$4.99 for 18 lb

The unit rate is $ ? /lb.

Answers

Answer:

4.99 divided by 18

0.277222222

Rounded to $0.28

Each year, a car loses 25% of the value it had the previous year. If the value of a car is $12,500 during the first year it is owned, which function represents the value of the car after y years

Answers

Answer:

T=12500-0.25y

Step-by-step explanation:

Step one:

given data

The value of the car is $12500.

let the value of the previous year be T

let the number of years be y

25% will be 0.25----this is equivalent to the gradient

The expression for the change in price can be represented linearly using the equation of a straight line,

y=mx+c

but since the price is reducing the expression becomes

y=-mx+c

Now, in this situation the expression for the cost after y years is

T=-(0.25y)+12500

rearrange

T=12500-0.25y

The expression is T=12500-0.25y

PLEASE HELP!! 15 POINTS AND BRAINLIEST !!

Answers

Answer:

40 degrees

Step-by-step explanation:

We need to find angle 3

Since angle 2 and angle 4 are vertical angles, they will be congruent

To solve for x we can make the following equation:

x+70=2x

x=70

In this problem angles 2 and 3 are supplementary (they add to 180)

Angle 2 is 140 degrees

We can now make the following equation to find angle 3 using measures addition postulate

let angle 3 be x

180-140=x

The 140 is angle 2

x=40

Your school band is performing a concert. Tickets cost $3 for students and $5 for adults. A total of 125 people attended the concert for a total ticket sales of $475. Write and solve a system of equations to find the number of students and adults that attended the concert. Make sure to write your answer in a complete sentence.

Answers

Given :

Tickets cost $3 for students and $5 for adults.

A total of 125 people attended the concert for a total ticket sales of $475.

To Find :

The number of students and adults that attended the concert.

Solution :

Let, number of students and adults that attended the concert is x and y.

Mathematical equation of given conditions :

x + y = 125    ....1)

3x + 5y = 425   ....2)

Putting value of x from 1 to equation 2 is :

3( 125 - y ) + 5y = 425

375 - 3y + 5y = 425

2y = 50

y = 25

x = 125 - 25

x = 100

Therefore, number of students and adults that attended the concert is 100 ans 25 respectively.

Hence, this is the required solution.

send the answer from 18 to 23 with process in copy​

Answers

19. Perimeter of rectangle = 2(l + b)

l = 25m

b = 16m

Perimeter of rectangular park = 2 (25 + 16)

= 50 + 32

= 82m

Perimeter of square park = 82m

(given that, perimeter of rectangular and square park are equal)

Perimeter of square = 4a

4a = 82

a = 82/4

a = 20.5m

Area of square park = a²

= 20.5²

= 420.25m²

20. Perimeter of regular hexagon = 6a

a = 2.5

6a = 6 × 2.5

= 15cm

21. Perimeter of regular decagon = 10a

a = 8

10a = 10 × 8

= 80cm

write 9/20 as a decimal

Answers

Answer:

0.45

Step-by-step explanation:

Divide 9 by 20.

A relay race is 1 3 4 miles long. Each relay team has 4 runners. If each runner runs the same distance in the race, how far will each runner run? Choose the correct answer.

Answers

Answer: 7/16

Step-by-step explanation:

Distance of the relay race = 1 3/4 miles

Number of runners for the relay team = 4 runners

Distance to be run by each runner will be:

= Distance of the relay race / Number of runners

= 1 3/4 ÷ 4

= 7/4 ÷ 4

= 7/4 × 1/4

= 7/16

Each runner will run 7/16 miles

n-3/4 = 2 3/4
(Change mixed number into a improper fraction)

Answers

Here’s the answer :)

Answer:

2 3/4 = 11/4 :)

Step-by-step explanation:

Whole number times denominator then add the numerator!

Hope this helps, marks as brainliest please!

An item is regularly priced at $60. It is on sale for 40% off the regular price. What is the sale price? ​

Answers

Answer: The sale price is $36.

Step-by-step explanation:

40% ÷ 100 = 0.4

0.4 × $60 = $24

$60 - $24 = $36

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

If there is an off of 40% on an item that cost $60.

The regular price of the item is $48.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

105 = 10/100 = 1/10

Example:

50% of 40 is 20.

50/100 x 40 = 20

25% of 100 is 25.

25/100 x 100 = 25.

We have,

Regular price = $60

Off = 40%

Sale price:

= 60 - (40% of 60)

= 60 - (40/100 x 60)

= 60 - (2/5 x 60)

= 60 - (2 x 12)

= 60 - 24

= $48

Thus.

If there is an off of 40% on an item that cost $60.

The regular price of the item is $48.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

use the function below to find f(-2).
f(x)=3^x

Answers

hi

f(x) = 3^(x)   so  (f-2) =    3^(-2)  =  1/ 3² =    1/9

Answer: 1/9

Step-by-step explanation:


M
6x-18
3x
J
B
K
Find the value of x

Answers

Answer: The value of x is 0.5?

Step-by-step explanation:

Will give 25 points! Please Explain! Im so confused! Big test on friday!

Write the slope-intercept form of an equation that passes through the given point and is perpendicular to the graph of the equation
(5,2), y=x-5

a. y=-x+7
b. y=3x+1
c. y=x+7
d. y=x+ 12/5

Please Dont forget to Also Explain! Thank You!

Answers

Answer:

a. y = -x + 7

Step-by-step explanation:

The line with equation y = x - 5 has slope = 1.

A perpendicular to a line has the opposite reciprocal slope of the line, so a perpendicular to the given line has slope -1.

y = -x + b

To find the value of b, we plug in the given point for x and y and solve for b.

y = -x + b

2 = -5 + b

b = 7

y = -x + 7

Answer: a. y = -x + 7

Markups The depth of water in a pond increases by 3% after a heavy rain. If the average depth of the water was 8.3 feet, what is the new depth?​

Answers

Answer: 8.55 feet

Step-by-step explanation:

We should equal the average depth to 1, so if it raises 3%, it raises 0.03. Simply add the original (1) plus what it rose (0.03) and multiply the original by that, so 8.3 × 1.03 = new depth. The result is 8.549 feets.

The line segment joining the points ( 3,-4) and (1,2) is trisected at the points P and Q . If the coordinates of P and Q are (p , -2 ) and ( 5/3 , q ) respectively, find the values of p and q.

Answers

Answer:

P = 7/3 and q = 0

Step-by-step explanation:

The given parameters are;

The endpoints of the segment are, (3, -4) and (1, 2)

The points that trisect the given points are P and Q with coordinates (p, -2) and (5/3, q) respectively

Therefore, we have;

The first point of the trisection cuts 1/3 of the length from one point and the second point of the trisection cuts 2/3 of the length from the same point

The coordinates of P or Q = (3 - (3 - 1)/3, -4 - (-4 - 2)/3) = (7/3 , -2)

Therefore, given that the y-coordinate value of the derived point coincides with the y-coordinate value of the point P, (p, -2) and there is only one point with x = -2 on the line, we have that the coordinate of the point P is (p, -2) = (7/3 , -2)

∴ P = 7/3

Similarly we have the second point of the trisection, Q, given as follows;

We are already given the x-coordinate value of the point Q as the 5/3 in (5/3, q)

Point Q = (5/3, q) = (3 - 2×(3 - 1)/3, -4 - 2×(-4 - 2)/3) = (5/3 , 0)

Point Q = (5/3, q) = (5/3 , 0)

∴ q = 0.

find y when y = 3x^2 -2x+5 and x = -1

Answers

Answer:

the answer is y=10

Given: F=(0,1),(2,4),(4,6),(6,8) and g=(2,5),(4,7),(5,8),(6,9),(7,5) (fxg)(2)

Answers

Answer:

(F-G)(x) = -1

Step-by-step explanation:

The notation (F - G)(x) means to subtract each function when x = 6. According to the sets when x = 6 then F is (6,8) and G is (6,9). To subtract the functions, subtract their output values. (F-G)(x) = 8 - 9 = -1.

Step-by-step explanation:

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[tex]f \times g = (2 \: , \:4 \times 5) \: , \: (4 \: , \: 6 \times 7) \: , \: (6 \: , \: 8 \times 9) \\ [/tex]

[tex]f \times g = (2 \: , \: 20) \: , \: (4 \: , \: 42) \: , \: (6 \: , \: 72) \\ [/tex]

_________________________________

Thus ;

[tex](f \times g)(2) = 20[/tex]

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Will give brainliest

Answers

Answer:

Y= -1/3x + 8/3

Step-by-step explanation:

 A police car drives 230 km in 2 1/2 hours. What is its average speed in kilometers per hour?​

Answers

Answer:

92 km/h

Step-by-step explanation:

does anyone know what's on the flvs 5.06 dba for Mrs. sujeily Witherspoon....have dba at 11:15

Answers

I'd go back through the lesson and take notes of steps in the last pages they give the review of the lesson, help full and a time saver. other than that I would try to write down all definitions and words listed in the module, but if you want to have a complete list of every thing go to the home page and get the guided notes, you can fill them out when looking back at the lesson.

if you have a short time to gather notes just go through and right down what you can, you can always keep the glossary open when doing a DBA. hope anyone who see's this does well :)

sorry I couldn't help much i was unaware of the course you are taking

Order the numbers from least to greatest.
Put the lowest number on the left.

1.001 1.101 0.113

Answers

0.113,1.001,1.101 This is the right answer

Answer:

I think this is answer:

0.113-1.001-1.101

Step-by-step explanation:

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