Question

Law of sines? .

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Answer 1

`\displaystyle 3,1 ≈ b`

Explanation:

First, find
`\displaystyle m∠C,`accourding to the Triangle-Sum Theorem:

`\displaystyle 180° = 32° + 69° + m∠C \hookrightarrow 180° = 101° + m∠C; 79 = m∠C`

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

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

`\displaystyle (c)/(sin∠C) = (b)/(sin∠B) = (a)/(sin∠A) \\ \\ (5,7)/(sin\:79°) = (b)/(sin\:32°) \hookrightarrow 3,0770743283... = (5,7sin\:32°)/(sin\:79°) \\ \\ 3,1 ≈ b`

I am joyous to assist you at any time.

Answer 2

b ≈ 3.1

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