Question

PLEASE HELP Law of sines: Which represents the value of c?

Answer 1

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.

Answer 2

ANSWER

$c = \frac{3 \sin(45 \degree)}{\sin(40 \degree)}$




EXPLANATION

The sum of the interior angles of the given triangle is
$180 \degree$


This implies that

$A + 95 \degree + 45 \degree = 180 \degree$


We group like terms to get,

$A = 180 - 140$


$A = 40 \degree$


The law of sines is given by,

$\frac{ \sin(A) }{a} = \frac{ \sin(B) }{b} = \frac{ \sin(C) }{c}$


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

We now substitute the values to get,

$\frac{ \sin(40 \degree) }{3} = \frac{ \sin(45 \degree) }{c}$

We reciprocate both sides of the equation to get,

$\frac{ 3}{\sin(40 \degree)} = \frac{ c }{\sin(45 \degree)}$


We now multiply both sides by
$\sin(45 \degree)$
to get,

$\frac{3 \sin(45 \degree)}{\sin(40 \degree)} =c$


or


$c = \frac{3 \sin(45 \degree)}{\sin(40 \degree)}$

The correct answer is B.