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PLEASE HELP
Law of sines:

Which represents the value of c?

PLEASE HELP Law of sines: Which represents the value of c?-example-1

2 Answers

3 votes
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.
User Iobelix
by
7.9k points
5 votes
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.

User Rafael Piccolo
by
8.9k points

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