Item 7

△ABC has vertices A(−1, 2), B(2, 8), and C(4, 1). Find the measure of each angle of the triangle. Round decimal answers to the nearest tenth.

Answers

Answer 1

Answer:

[tex]A = 74.7^\circ[/tex]

[tex]B = 42.5^\circ[/tex]

[tex]C = 62.8^\circ[/tex]

Step-by-step explanation:

Given

[tex]A = (-1,2) \to (x_1,y_1)[/tex]

[tex]B = (2,8) \to (x_2,y_2)[/tex]

[tex]C = (4,1) \to (x_3,y_3)[/tex]

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2[/tex]

For AB

[tex]A = (-1,2) \to (x_1,y_1)[/tex]

[tex]B = (2,8) \to (x_2,y_2)[/tex]

[tex]d = \sqrt{(-1 - 2)^2 + (2 - 8)^2[/tex]

[tex]d = \sqrt{(-3)^2 + (-6)^2[/tex]

[tex]d = \sqrt{45[/tex]

So:

[tex]AB = \sqrt{45[/tex]

For BC

[tex]B = (2,8) \to (x_2,y_2)[/tex]

[tex]C = (4,1) \to (x_3,y_3)[/tex]

[tex]BC = \sqrt{(2 - 4)^2 + (8 - 1)^2[/tex]

[tex]BC = \sqrt{(-2)^2 + (7)^2[/tex]

[tex]BC = \sqrt{53[/tex]

For AC

[tex]A = (-1,2) \to (x_1,y_1)[/tex]

[tex]C = (4,1) \to (x_3,y_3)[/tex]

[tex]AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2[/tex]

[tex]AC = \sqrt{(-5)^2 + (1)^2[/tex]

[tex]AC = \sqrt{26[/tex]

So, we have:

[tex]AB = \sqrt{45[/tex]

[tex]BC = \sqrt{53[/tex]

[tex]AC = \sqrt{26[/tex]

By representation

[tex]AB \to c[/tex]

[tex]BC \to a[/tex]

[tex]AC \to b[/tex]

So, we have:

[tex]a = \sqrt{53[/tex]

[tex]b = \sqrt{26[/tex]

[tex]c = \sqrt{45[/tex]

By cosine laws, the angles are calculated using:

[tex]a^2 = b^2 + c^2 -2bc \cos A[/tex]

[tex]b^2 = a^2 + c^2 -2ac \cos B[/tex]

[tex]c^2 = a^2 + b^2 -2ab\ cos C[/tex]

[tex]a^2 = b^2 + c^2 -2bc \cos A[/tex]

[tex](\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A[/tex]

[tex]53 = 26 +45 - 2 * 34.21 * \cos A[/tex]

[tex]53 = 26 +45 - 68.42 * \cos A[/tex]

Collect like terms

[tex]53 - 26 -45 = - 68.42 * \cos A[/tex]

[tex]-18 = - 68.42 * \cos A[/tex]

Solve for [tex]\cos A[/tex]

[tex]\cos A =\frac{-18}{-68.42}[/tex]

[tex]\cos A =0.2631[/tex]

Take arc cos of both sides

[tex]A =\cos^{-1}(0.2631)[/tex]

[tex]A = 74.7^\circ[/tex]

[tex]b^2 = a^2 + c^2 -2ac \cos B[/tex]

[tex](\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B[/tex]

[tex]26 = 53 +45 -97.67 * \cos B[/tex]

Collect like terms

[tex]26 - 53 -45= -97.67 * \cos B[/tex]

[tex]-72= -97.67 * \cos B[/tex]

Solve for [tex]\cos B[/tex]

[tex]\cos B = \frac{-72}{-97.67}[/tex]

[tex]\cos B = 0.7372[/tex]

Take arc cos of both sides

[tex]B = \cos^{-1}(0.7372)[/tex]

[tex]B = 42.5^\circ[/tex]

For the third angle, we use:

[tex]A + B + C = 180[/tex] --- angles in a triangle

Make C the subject

[tex]C = 180 - A -B[/tex]

[tex]C = 180 - 74.7 -42.5[/tex]

[tex]C = 62.8^\circ[/tex]


Related Questions

can someone please help its my 2 to last one

Answers

Answer:

x= -7 because when you add 60+45+82 you get 187. The interior angles of a triangle add up to 180

Step-by-step explanation:

The slating palace charges a $6.00 shoe rental fee plus $2.00 an hour to skate.Mathland skating rink charges $4.00 an hour to skate . what equation represents situation on;the skating palace

Answers

Answer:

Equation for the skating palace

= 6 + 2x

Step-by-step explanation:

Let the number of hours = x

For skating palace, the equation is written as:

The slating palace charges a $6.00 shoe rental fee plus $2.00 an hour to skate.

$6 + $2 × x

= 6 + 2x

For Mathland , the equation is written as:

Mathland skating rink charges $4.00 an hour to skate .

$4 × x

= 4x

Therefore, the equation that represents the situation on the skating palace is :

6 + 2x

Reflect the function f(x)=x^4 about the x-axis and translate it 3 units to the left to produce g(x). A. G(x)=-x^4+3 B. G(x)=-x^4-3 C. G(x)=-(x-3)^4 D. G(x)=-(x+3)^4

Answers

Answer:(d)

Step-by-step explanation:

Given

Function is [tex]f(x)=x^4[/tex]

If it is reflected about the x-axis it becomes [tex]-x^4[/tex]

To shift it 3 units to the left it becomes

[tex]-(x+3)^4[/tex]

option (d) is correct

This is shown in the figure below

Pls help is it; (1.5, 2) or no solution

Answers

Answer:

no solution?

Step-by-step explanation:

If sin 52° = 0.788, what is the approximate value of

cos 38°?

No link pls

Answers

Answer:

0.788

Step-by-step explanation:

Sin 52° = 0.788

Therefore

Cos 38° Is 0.788

The approximate value for 38° is 0.788

WHAT IS 1/2 + 1/9 PLEASE ANSWER! AND EXPLAIN I NEED MY GRADE UP!!!

Answers

Answer:

11/18

Step-by-step explanation:

1 2 + 1 9 = ? The Least Common Multiple (LCM) of 2 and 9 is 18. Multiply the numerator and denominator of each fraction by whatever value will result in the denominator of each fraction being equal to the LCM: 1 2 + 1 9 = 1 × 9 2 × 9 + 1 × 2 9 × 2 = 9 18 + 2 18 Now that the fractions have like denominators, add the numerators: 9 18 + 2 18 = 9 + 2 18 = 11 18 The result is: 1 2 + 1 9 = 11 18

so 11/18 is you answer

Answer:

11/18

Step-by-step explanation:

Get the common denominator by multiplying 2 and 9.

Multiply both sides of 1/2 by 9 to get 9/18, and both sides of 1/9 by 2 to get 2/18.

[tex]\frac{1}{2} +\frac{1}{9} = \frac{9}{18} + \frac{2}{18} = \frac{11}{18}[/tex]

After adding both fractions you'll get 11/18. That's your answer.

Write the first five terms of the geometric sequence, given a1= -16 and r= -1/4​

Answers

Answer: -16, 4, -1, 1/4,?

Step-by-step explanation: the nth term of a GP is given by Un= ar^n-1

Where n= the term.

So substituting the values for each term will give you the answer above. I don't know if it's tiredness or what but my fifth term gives me the same value as my fourth term.

Find the length of the boldest arc. Rounded answer to the nearest hundredth (use 3.14 for pie)​

Answers

Answer:
8π yards
Step-by-step explanation:
A circle subtends a total angle of 360 ° from its center.The length of an arc is directly proportional to the angle it subtends from the circle's center. The arc's length can therefore be calculated as:
C=πd=2πr
Where C is circumference, d is diameter and r is radius. Given r as 16 yards then the arc length which is equivalent to circumference is given as


Identify the volume of a regular hexagonal pyramid with base edge length 8 in. and height 10 in.,
rounded to the nearest tenth.

Answers

Answer:

554.3 m^2

Step-by-step explanation:

https://brainly.com/question/17542967?referrer=searchResults

The volume of a regular hexagonal pyramid will be 554.3 cubic inches.

What is the volume of the pyramid?

Let h be the height of the pyramid, l be the slant height, and A be the base area of the pyramid. Then the volume of the pyramid will be given as,

Volume = (1/3) × A × h

The base area is calculated as,

A = 6 x (1/2) x 8 x 8 x sin 60°

A = 3 x 8 x 8 x 0.866

A = 166.28 square inches

The volume of a regular hexagonal pyramid is calculated as,

V = 1/3 x 166.28 x 10

V = 554.3 cubic inches

More about the volume of the pyramid link is given below.

https://brainly.com/question/17615619

#SPJ2

What is the correct answer?

Answers

pink , pink is always right

Answer:

pink

Step-by-step explanation:

,pink is the only logical option

State if the triangles in each pair are similar.

Answers

If two triangles have two pairs of sides in the same ratio and the included angles are also equal, then the triangles are similar.

Someone please help with this question I need an answer no longer than 5 minutes

NO LINKS

Answers

Answer:

radius: 8.4   Area: 221.5

Step-by-step explanation:

16.8 divided by 2 = 8.4

The Formula for finding the area of circle= R₂ (radius squared: radius times itself) Multiplied by pi. pi = 3.14

8.4₂ multiplied by 3.14

What is the value of s?

Answers

The answer is 17. Let me know if you need an explanation

Please HEELLPPP!!!!!!!!!

Answers

Answer:

C) 56

Step-by-step explanation:

These angles are supplementary (they add up to 180):

3x + 31 + 2x - 6 = 180

5x + 25 = 180

5x = 180 - 25

5x = 155

x = 31

<FEG:

2x - 6

2(31) - 6

62 - 6

56

Which is the best estimate for √34 to the nearest whole number​

Answers

Answer:Other than using a calculator to get an approximate value (

5.83

) for  

34

,  

34

can not be simplified

Step-by-step explanation:The only factors (

>

1

) of  

34

are  

2

and  

17

Since neither of these are a square,  

34

has no simplification.

What is m X to the nearest degree?
Help plssss

Answers

Answer:

A

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos X = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{XY}{XZ}[/tex] = [tex]\frac{13}{18}[/tex] , then

∠ X = [tex]cos^{-1}[/tex] ([tex]\frac{13}{18}[/tex] ) ≈ 44° ( to the nearest degree ) → A

The answer to your question is A

Are the two Rectangles congruent? How do you know?

A. No, Sides are diffrent length and do not have a corresponding part.
B. Yes, each side and each angle has a congruent corresponding part. ​

Answers

Yes each side and each angle has a congruent corresponding part

Which polynomial is a perfect square trinomial?
36x2 − 18x − 9


4a2 − 28a − 49


25b2 − 40b + 16


4x2 − 6x + 9

Answers

Answer:

The third one

Step-by-step explanation:

The process would be figuring out the square root of the first and last term of each equation, after doing so, you would take that number (square root of first and last number) then you do 2(a)(b) which would be which should be the middle term. In this case 2(5)(4) = 40 which is correct.

Step-by-step explanation:

my calculator got 36x*2-18-27/4

Name all the expressions that are equivalent to 3x+6y+7x-14
Select all
A.) -10x-14
B.)2(2x + 3y - 7)
C.)4x - 6y + 14
D.)4x+6y - 14
E.)10x + 6y - 14

Answers

Answer:

The answer to the question is E

Step-by-step explanation:

E is the only answer out of the choices to be equivalent to 3x+6y+7x-14

The midpoint of AB is M(0,3). If the coordinates of A are (4, -1), what are the
coordinates of B?
Answer:
Submit Answer
attempt 1 out of 2

Answers

The coordinates of B are (-4, 7).

Evaluate the expression when a=6 and b = 50.
b-4a

Answers

Answer:

26

Step-by-step explanation:

sub it it

50-(4×6)

50-24

the answer is 4 dhuenwk

Cards in a pack are black or red in the ratio
black: red = 2:5
What fraction of the cards are red?

Answers

1/3 fraction of the cards is red

A camera has a listed price of $511.99 before tax. If the sales tax rate is 7.75%, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary,

Answers

Answer:

$551.70

Step-by-step explanation:

Price before tax= $511.99

Cost of the tax= 7.75/100×511.99

= $39.679

Total cost of the camera= $511.99+$39.679

= $551.669

≈ $551.70

The box plots show the weights in pounds of the dogs in two different animal shelters

Weights of Dogs in Shelter A

6

8

10

12

14

16

18

20

22

24

26

28

Weights of Dogs in Shelter B

One-half of the dogs in each shelter are between which weights?

between 8 and 30 pounds in shelter A between 10 and 28 pounds in shelter B

benveen 8 and 17 pounds in shelter A between 10 and 16 pounds in shelter B

between 21 and 30 pounds in shelter A between 18 and 28 pounds in shelter B

between 28 and 30 pounds in shelter A between 20 and 28 pounds in shelter B

Answers

Answer:

between 21 and 30 pounds in shelter A between 18 and 28 pounds in shelter B

Step-by-step explanation:

One half of the dogs in each shelter points at the the upper 50% of the dog weight. This point is marked by the median value up to the maximum weight value.

The median value is the point marked inside the box on a boxplot and the maximum value is the upper end or the endpoint of the whisker.

For SHELTER A:

Median = 21

Maximum = 30

Hence, For shelter A, it is the interval between 21 and 30

For shelter B:

Median = 18

Maximum = 28

Hence, it is the interval between 18 and 28

Answer:

it's c

Step-by-step explanation:

:)

(add. write your answer as a fraction, as a whole or as a mixed number)
PLEASE HELP . WILL GIVE BRAINLIEST !

Answers

Answer:

3 and 1/12

Step-by-step explanation:

hope this helps! :)

Round your answer to the nearest hundredth.
A
4.
?
B
С
3

Answers

Answer:

a. 4.00

b. 3.00

I hope this helps

Please please please help me with this

Answers

it’s a black screen

Answer:

Apparently the picture is pitch black so I don't understand what you need help with. Sorry.

Step-by-step explanation:

28 out of the 50 students in the 4th grade love chocolate ice cream. What percentage of the 4th graders DO NOT love chocolate ice cream?

Answers

Answer:20%

Step-by-step explanation: multiply 40 x 50=2,000

2,000 divided by 100= 20%

Where do people and animals get the oxygen they breathe?

From plants

From other animals

From water

From the sun

Answers

Answer:

From plants

hope it helps you have a good day keep smiling be happy stay safe ☺️

Answer:

From Plants

Hope it will help you

Solve 3x2 + x - 10 = 0. Round solutions to the nearest hundredth. (5 points) a x ≈ −5 and x ≈ 2 b No real solutions c x ≈ −2 and x ≈ 1.67 d x ≈ −1.67 and x ≈ 2

Answers

Answer:

c) x ≈ −2 and x ≈ 1.67

Step-by-step explanation:

Solve 3x²+ x - 10 = 0.

We solve using Almighty formula

-b ± √b² - 4ac/2a for equation: ax² + bx + c

where a = 3, b = 1, c = -10

Hence

-1 ± √1² - 4 × 3 × -10/2 × 3

-1 ± √1 - (-120)/6

-1 ± √1 + 121/6

-1 ± √121/6

-1 ± 11/6

Hence:

-1 - 11/6

-12/6 = -2

-1 + 11/6

= 10/6

= 1.67

Therefore, x = -2, x = 1.67

Option c) x ≈ −2 and x ≈ 1.67 is the correct answer

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