Respuesta :

absor201

Answer:

Option D is correct.

Step-by-step explanation:

We are given c = 12

m∠B = 27°

a = 9

We need to find b

We would use Law of Cosines

[tex]b = a^2 + c^2 -2ac\,cosB[/tex]

Putting values and solving

[tex]b^2 = (9)^2 + (12)^2 -2(9)(12)\,cos(27°)\\b^2 = 81 + 144 - 216(0.891)\\b^2 = 81 + 144 - 192.456\\b^2 = 32.54\\taking\,\,square\,\,roots\,\,on\,\,both\,\,sides\\\\\sqrt{b^2} = \sqrt{32.54}\\ b = 5.7[/tex]

So, Option D is correct.

Answer:

D. 5.7

Step-by-step explanation:

We have been given that in △ABC,c=12, m∠B=27°, and a=9. We are asked to find the value of b.

We will use law of cosines to solve for b.

[tex]b^2=a^2+c^2-2ac\cdot \tect{cos}(B)[/tex]

Upon substituting our given values in law of cosines, we will get:

[tex]b^2=9^2+12^2-2\cdot 9\cdot 12\cdot {cos}(27^{\circ})[/tex]

[tex]b^2=81+144-216\cdot 0.891006524188[/tex]

[tex]b^2=225-192.457409224608[/tex]

[tex]b^2=32.542590775392[/tex]

Now, we will take square root of both sides of our equation.

[tex]b=\sqrt{32.542590775392}[/tex]

[tex]b=5.70461136059[/tex]

[tex]b\approx 5.7[/tex]

Therefore, the value of b is 5.7 and option D is the correct choice.

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