Two sides of a triangle have measures 3 ft and 6 ft. Also, these sides form a vertex whose angle measures 60 degrees. Calculate the missing attributes of the triangle.

Answers

Answer 1

Answer:

A. The length of the third side is approximately 5 feet.

B. A = [tex]88^{o}[/tex], B = [tex]60^{o}[/tex] and C = [tex]32^{o}[/tex].

Step-by-step explanation:

Let the triangle be ABC. Given two sides and an included angle, let us apply the cosine rule to determine the third length.

A. Let side a = 6 feet and c = 3 feet, thus;

[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] - 2ac Cos B

  = [tex]6^{2}[/tex] + [tex]3^{2}[/tex] - 2(6 x 3) Cos [tex]60^{o}[/tex]

  = 36 + 9 - 36 x 0.5

  = 45 - 18

[tex]b^{2}[/tex] = 27

b = [tex]\sqrt{27}[/tex]

  = 5.1962

b  = 5.2 feet

b ≅ 5 feet

The length of the third side is approximately 5 feet.

B. Given that B = [tex]60^{o}[/tex], then let us apply the Sine rule to determined the measure of A.

[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex]

So that,

[tex]\frac{6}{Sin A}[/tex] = [tex]\frac{5.2}{Sin60^{o} }[/tex]

Sin A = [tex]\frac{0.886*6}{5.2}[/tex]

Sin A = 0.99923

A = [tex]Sin^{-1}[/tex] 0.99923

  = 87.75

A ≅ [tex]88^{o}[/tex]

Since the sum of angle in a triangle = [tex]180^{o}[/tex].

Then,

A + B + C = [tex]180^{o}[/tex]

[tex]88^{o}[/tex] + [tex]60^{o}[/tex] + C = [tex]180^{o}[/tex]

[tex]148^{o}[/tex] + C = [tex]180^{o}[/tex]

C = [tex]180^{o}[/tex] - [tex]148^{o}[/tex]

     = [tex]32^{o}[/tex]

C = [tex]32^{o}[/tex]

Thus,

A = [tex]88^{o}[/tex], B = [tex]60^{o}[/tex] and C = [tex]32^{o}[/tex].


Related Questions

PLEASE HELP ME HURRY

Answers

2/5 of the class is male

40% of the class is male

3/5 of the class is female

60% of the class is female

Not sure if this is right, but this is what I got.

Solve and Graph: 12 – ⅔ x > 6

Answers

Answer:

There's the graph

But the answer is x<9

X is all values below 9.

Danielle is making a quilt with triangles and squares. There are 4 colored triangles inside each square. The base and height of each triangle is x + 4 inches as shown. Which polynomial represents the area of the colored triangles in square inches?

Answers

Answer:

[tex](2x^2+16x+32)\ \text{sq. inches}[/tex]

Step-by-step explanation:

b = h = Base = Height of triangle = [tex](x+4)\ \text{inches}[/tex]

Area of one triangle

[tex]A=\dfrac{1}{2}bh=\dfrac{1}{2}(x+4)(x+4)[/tex]

There are 4 colored triangles so total area of the triangles is

[tex]4A=4\times \dfrac{1}{2}(x+4)(x+4)\\\Rightarrow 4A=2(x+4)^2\\\Rightarrow 4A=2(x^2+8x+16)\\\Rightarrow 4A=2x^2+16x+32[/tex]

The area of the colored triangles is [tex](2x^2+16x+32)\ \text{sq. inches}[/tex]

please show work
23 lbs of onions cist $250.70. How much will 50 lbs cost

Answers

Answer:

$545.00

Step-by-step explanation:

250.7 / 23 = 10.9

$10.9 is the cost of every lb of onions.

Then we multiply 10.9 by 50 because there are 50 lbs. like this

10.9 * 50 = 545

So $545.00 is our answer.

it is $545.00 hope this helps

HELP MEEE PLEASEEEEE!!!!! I NEED HELPPP!!

Which the ordered pair that is a solution of the system for linear equations?​

Answers

Answer:

(2,2)

Step-by-step explanation:

Lets check:

(2,2)

2(2)-2=2 Correct !

2=-2+4 correct !

Hope this helps plz hit the crown :D

Answer:

i believe the answers (2,2)

Step-by-step explanation:

if you add it in for y and x  you will see it right

I need help pleaseee

Answers

Oof that looks really hard sorry can’t help but wish u good luck...

What is the solution to the system graphed below?

Answers

Answer:

I'm pretty sure it is (2,0)

**FIRST CORRECT ANSWER GETS BRAINLEST**
y varies directly as x, and y = 0.5 when x = 0.4.
A.) y = 4/5 x
B.) y = 0.1 x
C.) y = 5/4 x
D.) y = 0.9 x

Answers

Answer:

C.) y = 5/4 x

Step-by-step explanation:

5/4 multiplied by 0.4 is 0.5

I went to get dinner at a restaurant. The bill for the meal was $60. I want to
leave a 20% tip. What will be my total cost including the tip? *

Answers

60 * 0.20 = $12
60 + 12 = $72
The total cost would be $72

can anyone help with this question

Answers

Step-by-step explanation:

GCF of 2 prime numbers is always 1, because prime number only have two factors, themselves and 1.

LCM of 2 prime numbers will be simply multiplying them together.

Answer:

Sasha can do that by; finding the HCM of two factors.

Razi will tell Jake to find the LCM you have to find the least common factor of the numbers,and then that's your answer.

Explanation:

Hope this helps:)!

Let x=
-
11
8
and y=
11
4
0
Which expression has a negative value?
Copyright 2017 Open Up Resources
Select one
OA. x+y
OB. xy
OC. x.y
OD. x/y

Answers

Answer:

OD. x/y

Step-by-step explanation:

The value of a new car decreases by about 15% in the first year. How much will a car be worth after one year if its initial value was $1,500? If you get stuck, consider using diagrams or a table to organize your work.

Answers

Answer:

$12,750

Step-by-step explanation: when you do the math you get it your welcome my G

Carrie read a total of 18 books over 6 months. If Carrie has read 30 books so far, how many months has she been with her book club? Assume the relationship is directly proportional.

? months

Answers

Answer:

10 months

Step-by-step explanation:

If we divide 18 and 6, you would get 3. This means that Carrie reads 3 books per month and we can divide 30 and 3 to figure out how many months that she read which is 10.

A point on the ocean floor is 5,962 m below sea level. Express this elevation as an integer.
the elevation as an integer is ___ m.

Answers

Answer:

-5,962 m

Step-by-step explanation:

Since the point is below sea level, it will be a negative number as an integer.

it is 5,962 m below sea level, so as an integer, it will be -5,962 m.

So, the elevation as an integer is -5,962 m

After adding a tip, the total lunch cost was $32.24. What percentage tip did they give? Enter your answer to the nearest percentage. the original cost was 27.32

Answers

15-15.5% it’s abt Arond there

CAN YOU HELP ME???
Laura borrowed $105,000 at a rate of 6% simple interest for 12 years. How much interest will Laura pay?
Group of answer choices

$75,600

$37,800

$180,600

$256,200

Answers

Answer:

Laura will pay an interest of  $75,600.

Step-by-step explanation:

Our formula: A = P(1 + rt)

Principal = $105,000

Rate = 6%

Time = 12 years

A (amount)= 105,000(1 + (0.06 × 12)) = 180,600

$180,600 - $105,000 = $75,600.

there are 50 kilometers in 31 miles. which representation does NOT show the same relationship?

Answers

Answer:

There's no options

Step-by-step explanation:

Answer:

Options please

Step-by-step explanation:

What’s the equation?

Answers

The answer is option 2 because if you were to plug in both values for m, you would exactly get the corresponding value for c.

HELP PLEASE!!!! I need someone to help me!!!!

Answers

Answer:

A

Step-by-step explanation:

Answer:

It's C or the one u just clicked on

Step-by-step explanation:

please help it's the SLOPE

Answers

Answer:

3/2

Step-by-step explanation:

do rise over run

rise is 3

run is 2

3/2

hope this helps <3

Answer:

slope is 1.5

Step-by-step explanation:

slope=rise over run

3/2=1.5

look at point

(1,-3) then go up 3 and right 2

lands in point

(3,0)

4x-y= -2
2х + Зу = 13

Answers

Answer:

x = 1/2

y = 4

Step-by-step explanation:

4x - y = -2     --------------------(I)

2x + 3y = 13 --------------------(II)

Multiply equation (I) by 3 and then add

(I)*3         12x - 3y = -6

(II)             2x  + 3y = 13           {Now add and so y will be eliminated}

               14x         = 7

                          x = 7/14

x = 1/2

Plugin x = 1/2  in equation (I)

[tex]4*\frac{1}{2}-y = -2[/tex]

  2 - y = -2

     -y  = -2 - 2

     -y = -4      

   y = 4

Answer:

x=1/2

y=4

Step-by-step explanation:

4x-y=-2

-y=-4x-2

y=4x+2

2x+3y=13

2x+3(4x+2)=13

2x+12x+6=13

14x=7

x=1/2

y=4x+2

y=4(1/2)+2

y=2+2

Y=4

Solve for x. assume that lines which appear to be diameters are actual diameters.

Answers

Answer:

x=10

Step-by-step explanation:

5x+17 = 67

The angles are vertical angles which means they are equal.  This means the arc lengths are equal

5x+17-17 = 67-17

5x = 50

5x/5 = 50/5

x =10

Determine the nth term rule and find the 45th term for the arithmetic sequence with a10=1 and d=−6.

Answers

Answer:

a(45) =-209

Step-by-step explanation:

a(n) = a +(n-1)d

d=-6

we have to get a1

By using:

a(10) = a1 +(10-1)-6=1

a(10) = a1 +(9)-6 =1

          a1  =1+54=55

So:a(45) = 55 +(45-1)-6=-209

hope this helps

Can someone do this please

Answers

ok so umm you need to do 5x4= 20 and divide 20 and 4 you get 5 and multiply 5x4 you get 20 and the answer is 20

what is the answer to 2.6=-0.2t

Answers

Answer:

-13

Step-by-step explanation:

Answer:

t = -13

Step-by-step explanation:

2.6 = -0.2t         Equation

2.6 / -0.2 . = -0.2t/-0.2          Divide -0.2 on both sides

t = - 13       Simplify

Leah would like to earn at least $120 per month. She babysits for $5 per hour and works at an ice cream shop for $8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop. How did you determine the pair(s) (x, y) that Leah could work to meet the given conditions in item 15?

Answers

Answer:

Babysitting= 13.3 hours

Icecream shop= 6.6 hours

Step-by-step explanation:

Step one:

let the hours for babysitting be x

and the hours for icecream shop be y

we are told that Leah would like to earn $120 monthly

She babysits for $5 per hour and

works at an ice cream shop for $8 per hour

5x+8y=120---------------1

Leah cannot work more than a total of 20 hours per month

x+y≤20-------------2

The system of equation for the situation is

5x+8y=120

x+y≤20

x=20-y

put x=20-y in eqn 1

5(20-y)+8y=120

100-5y+8y=120

3y=120-100

3y=20

y=20/3

y=6.6 hours

put y=6.6 in eqn 2

x+6.6≤20

x≤20-6.6

x=13.3hours

A recipe requires 1/3 cup of milk for each 1/4 ounce of sugar. How many ounces of sugar are needed for each cup of milk? Answer quickly please!

Answers

Answer: 3/4 ounces of sugar for one cup.

Step-by-step explanation: Since we know that we have 1/3 cup, we can simply times the 1/4 by 3. If it helps, just imagine pouring 1/4 ounce of sugar three times.

Hope this helps :)

The graph shows the cost of buying tickets to a concert.
What is the cost of buying 10 tickets?

Answers

It doesn’t say anything post another question

please answer this. thank you

Answers

I wanna ruin our friendship we should be lovers instead

pls help me fast like asap

Answers

D is your answer because you gave 20 and they are subtracting the cost of 3x lbs of apples

Answer:

Im pretty sure its D

Step-by-step explanation:

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