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

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? *

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60 * 0.20 = $12
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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

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What is the solution to the system graphed below?

Answers

Answer:

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

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:

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

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

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

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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:

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.

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Answers

Answer:

There's the graph

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Answer:

3/2

Step-by-step explanation:

do rise over run

rise is 3

run is 2

3/2

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Answer:

slope is 1.5

Step-by-step explanation:

slope=rise over run

3/2=1.5

look at point

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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.

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

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Answer:

x=1/2

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Step-by-step explanation:

4x-y=-2

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Answers

Answer:

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Step-by-step explanation:

Answer:

t = -13

Step-by-step explanation:

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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

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Answers

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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:

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The graph shows the cost of buying tickets to a concert.
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Answers

It doesn’t say anything post another question

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

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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

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x+y≤20-------------2

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Answers

Answer:

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Step-by-step explanation:

Answer:

Options please

Step-by-step explanation:

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Answers

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Answers

Answer:

A

Step-by-step explanation:

Answer:

It's C or the one u just clicked on

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

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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

**FIRST CORRECT ANSWER GETS BRAINLEST**
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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

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