Question

PLEASE HELP
Law of sines:

Which represents the value of c?

Answer 1

ANSWER


`c = (3 \sin(45 \degree))/(\sin(40 \degree))`




Step-by-step 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,


`( \sin(A) )/(a) = ( \sin(B) )/(b) = ( \sin(C) )/(c)`


Based on our known values, we use,

`( \sin(A) )/(a) = ( \sin(C) )/(c)`

We now substitute the values to get,


`( \sin(40 \degree) )/(3) = ( \sin(45 \degree) )/(c)`

We reciprocate both sides of the equation to get,


`( 3)/(\sin(40 \degree)) = ( c )/(\sin(45 \degree))`


We now multiply both sides by

`\sin(45 \degree)`
to get,


`(3 \sin(45 \degree))/(\sin(40 \degree)) =c`


or



`c = (3 \sin(45 \degree))/(\sin(40 \degree))`

The correct answer is B.

Answer 2

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.