Respuesta :

sqdancefan

Answer:

  b ≈ 3.1

Step-by-step explanation:

The law of sines tells you ...

  b/sin(B) = c/sin(C)

Here, you have to find angle C based on the sum of the angles of a triangle being 180°.

 C = 180° - A - B = 180° - 69° - 32° = 79°

Multiplying the above law of sines equation by sin(B), you have ...

  b = c·sin(B)/sinc(C) = 5.7·sin(32°)/sin(79°) ≈ 3.07707

  b ≈ 3.1 . . . . . rounded to tenths

BasketballEinstein

Answer:

[tex]\displaystyle 3,1 ≈ b[/tex]

Step-by-step explanation:

First, find [tex]\displaystyle m∠C,[/tex]accourding to the Triangle-Sum Theorem:

[tex]\displaystyle 180° = 32° + 69° + m∠C \hookrightarrow 180° = 101° + m∠C; 79 = m∠C[/tex]

Now that we have all three angles, we can solve for edge b

[the second edge], using the Law of Sines:

[tex]\displaystyle \frac{c}{sin∠C} = \frac{b}{sin∠B} = \frac{a}{sin∠A} \\ \\ \frac{5,7}{sin\:79°} = \frac{b}{sin\:32°} \hookrightarrow 3,0770743283... = \frac{5,7sin\:32°}{sin\:79°} \\ \\ 3,1 ≈ b[/tex]

I am joyous to assist you at any time.

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