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Zina [86]
3 years ago
13

Suppose a triangle has two sides of length 42 and 35, and that the angle between these two sides is 120 degrees. What is the len

gth of the third side of the triangle?
Mathematics
1 answer:
FrozenT [24]3 years ago
7 0

Answer:

Option D

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other and the given angle is the included angle. This means that the angle is formed by the intersection of the two lines. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:

b^2 = a^2 + c^2 - 2*a*c*cos(B).

The question specifies that a=42, B=120°, and c=35. Plugging in the values:

b^2 = 42^2 + 35^2 - 2(42)(35)*cos(120°).

Simplifying gives:

b^2 = 4459.

Taking square root on the both sides gives b = 66.78 (rounded to the two decimal places).

This means that the length of the third side is 66.78 units!!!

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PLEASE HELP ASAP!!!!
yanalaym [24]

Answer:

a = -4

b = 3

c = 6

Step-by-step explanation:

x^2 + 8x = 38

We take the coefficient of the x term

Divide by 2 and then square it

8/2 =4

4^2 = 16

Add 16 to both sides

x^2 +8x + 16 = 38 + 16

x^2 +8x +16 = 54

Take b/2 and use it in the the (x+b/2)^2

(x+4)^2 = 54

Take the square root of each side

sqrt((x+4)^2) = ± sqrt(54)

x+4 =  ± sqrt(54)

Subtract 4 from each side

x+4-4 = -4  ± sqrt(54)

x = -4  ± sqrt(54)

Simplify the square root

x = -4  ± sqrt(9*6)

x = -4 ± sqrt(9) sqrt(6)

x = -4 ± 3 sqrt(6)

8 0
3 years ago
Calculator
MariettaO [177]

Answer:

{84mm}^{2}

Step-by-step explanation:

Area of square= l×l

Area of square= 6mm × 6mn

Area if square = 36 mm²

Area of triangle 1= ½b ×h

Area of triangle 1= ½ (6mm)(8mm)

Area of triangle 1 = 24 mm²

Area of triangle 2 is the same as area of traingle 1 because they have the same base and hight

: . area of triangles is 48mm²

Area of the figure= Area of square + Area of triangles

A of figure = 36+48

A of figure = 84 mm²

Option 2

Use trapezium formula

Area of trapezium= (a+b)/2 * h

a=6 mm (base)

b=8+6=14 mm (Base)

h= 6mm (height)

area \: of \: trapezium = ( \frac{6 + 14}{2} )(6) \\  = 60mm ^{2}

Therefore the area of triangle= 24mm² as calculated in option 1

Area of the figure= Area of trapezium +Area of triangle

Area of figure = 60+24

= 84 mm²

4 0
3 years ago
Helppppp me pleaseeeee
DerKrebs [107]

Answer:

D

Step-by-step explanation:

Congruent angles are identical in number of degrees.

6 0
4 years ago
1. Melinda's fudge recipe calls for 34 cup of butter for one batch of fudge. She plans to make 8 batches. How many cups of butte
zhuklara [117]

Answer:

272 cups

Step-by-step explanation:

so you need 34 cups for one batch if you need to make 8 batches then you would need to multiple them to find the answer.

34*8=272

8 0
3 years ago
The list price is $74.13. Trade discount of 7/21. Find net cost
bonufazy [111]

Answer: Net\ cost=\$49.42

Step-by-step explanation:

You need to analize the information given in the exercise.

In this case you know that the List price is:

List\ price=\$74.13

And, based on the data given, you also know that the Trade discount is:

Trade\ discount=\frac{7}{21}

Then, the first step you need to apply is to multiply the List price by the Trade discount, as you can observe below:

(\$74.13)\frac{7}{21}=\$24.71

 Now it is important to remember that, by definition, the Net cost can be found by subtracting the List price  (which in this case is $74.13) and the product of the List price and the Trade discount (which in this case is $24.71).

Then, through this procedure, you get the following Net cost:

Net\ cost=\$74.13-\$24.71\\\\Net\ cost=\$49.42

7 0
3 years ago
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