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oksian1 [2.3K]
3 years ago
15

Solve the Law of Cosine: c^2 = a^2+ b^2 - 2abcosC for cos C.

Mathematics
1 answer:
Andrew [12]3 years ago
6 0

Answer:

The Law of Cosine :  cos C = \frac{a^{2}+ b^{2}-c^{2}}{2ab}

Step-by-step explanation:

See the figure to understand the proof :

Let A Triangle ABC with sides a,b,c,

Draw a perpendicular on base AC of height H meet at point D

Divide base length b as AD = x -b   and    CD = x

By Pythagoras Theorem

In Triangle BDC             And     In Triangle BDA

a² = h² + x²     (  1  )                        c² = h² + (x-b)²

                                                      c² = h² + x² + b² - 2xb   ...(. 2)

From above eq 1 and 2

c² = (a² - x²) + x² + b² - 2xb

or, c² = a² + b² - 2xb                    .....(3)

Again in ΔBDC

cos C = \frac{BD}{BC}

Or, cos C = \frac{x}{a}

∴ x= a cos C

Now put ht value of x in eq 3

I.e, c² = a² + b² - 2ab cos C

Hence , cos C = \frac{a^{2}+ b^{2}-c^{2}}{2ab}      Proved   Answer

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Answer:

6

Step-by-step explanation:

All sides of triangle EFD have x6 of BAC.

E.g.: BA = 2. ED = 2 x 6 = 12

8 0
3 years ago
What is 16x9+67x9 can someone help me?
vazorg [7]

Answer: 747


Step-by-step explanation:

16x9+67x9

First multiply 16 and 9 which is equal to 144

144+67x9

now multiply 67 and 9 which is equal to 603

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Now add 144 and 603 which is equal to 747

So the answer to 16x9+67x9 is 747




5 0
3 years ago
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HELP PLEASE!!!!!! Only 5 more minutes till i turn it in!!!
GarryVolchara [31]

Answer:

<B = 70°

Step-by-step explanation:

First we need to find x, lets plugin these two equations.

2x - 30 = x + 20

Then find like terms

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Then we plugin 50 for x

2(50) - 30 =

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5 0
2 years ago
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If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be p
andrey2020 [161]

Answer:

b. 300x1 + 125x2 < = 4,000

Step-by-step explanation:

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This means that the the total amount of labor has to be of at most 4,000, that is:

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300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor

The total amount of labor is:

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Uniting the two equations:

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And thus the correct answer is given by option b.

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2 years ago
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