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MrEquation
Answer:  3sin(45) over sin(40)

Using the law of sins that is given, you can write the following proportion.
3/sin(40) = c/sin(45)

All you have to do to solve for C is to multiply by sin(45). In the proportion, the letter are the side lengths and the trig ratios are of the angle opposite the side.

kudzordzifrancis
ANSWER

[tex] c = \frac{3 \sin(45 \degree)}{\sin(40 \degree)} [/tex]




EXPLANATION

The sum of the interior angles of the given triangle is
[tex]180 \degree[/tex]


This implies that

[tex]A + 95 \degree + 45 \degree = 180 \degree[/tex]


We group like terms to get,

[tex]A = 180 - 140[/tex]


[tex]A = 40 \degree[/tex]


The law of sines is given by,

[tex] \frac{ \sin(A) }{a} = \frac{ \sin(B) }{b} = \frac{ \sin(C) }{c} [/tex]


Based on our known values, we use,
[tex] \frac{ \sin(A) }{a} = \frac{ \sin(C) }{c} [/tex]

We now substitute the values to get,

[tex] \frac{ \sin(40 \degree) }{3} = \frac{ \sin(45 \degree) }{c} [/tex]

We reciprocate both sides of the equation to get,

[tex] \frac{ 3}{\sin(40 \degree)} = \frac{ c }{\sin(45 \degree)} [/tex]


We now multiply both sides by
[tex] \sin(45 \degree) [/tex]
to get,

[tex] \frac{3 \sin(45 \degree)}{\sin(40 \degree)} =c[/tex]


or


[tex] c = \frac{3 \sin(45 \degree)}{\sin(40 \degree)} [/tex]

The correct answer is B.

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