Respuesta :

eunice1234

Answer: [tex]\Large\boxed{C.~21}[/tex]

Step-by-step explanation:

The goal of the question

Find the value of 2abcosC

Given information

a = 4

b = 3

c = 2

Given formula (Law of Cosine)

[tex]c^2=a^2+b^2-2abcosC[/tex]

Substitute values into the formula (Leave 2abcosC as it is)

[tex](2)^2=(4)^2+(3)^2-2abcosC[/tex]

Simplify the exponents

[tex]4=16+9-2abcosC[/tex]

Simplify by addition

[tex]4=25-2abcosC[/tex]

Add 2abcosC on both sides

[tex]4+2abcosC=25-2abcosC+2abcosC[/tex]

[tex]4+2abcosC=25[/tex]

Subtract 4 on both sides

[tex]4 + 2abcosC-4=25-4[/tex]

[tex]\Large\boxed{2abcosC=21}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

C

Step-by-step explanation:

a² + b² - 2abcosC = c² ( subtract a² + b² from both sides )

- 2abcosC = c² - a² - b² ( multiply through by - 1 )

2abcosC = a² + b² - c²

a, b, c are the sides opposite vertices A, B, C

here a = 4 , b = 3 , c = 2 , then

a² + b² - c²

= 4² + 3² - 2²

= 16 + 9 - 4

= 25 - 4

= 21

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