Question

Which of the following cannot be derived from the law of sines?

Answer 1

What is the law of sines?

Answer 2

dont know.... lol that why i asked

Answer 3

hahaha... I don't know either. That is why I asked you about the law before considering which one is the correct one. Can you google it?

Answer 4

lmfao.. yea i did man! i got nuthin! imma fail this test !

Answer 5

Law of Sines

\(\large \dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C} \)

Answer 6

A. The first choice is just the first two fractions of the law of sines, so it certainly can be derived from the law of sines.

Answer 7

Now look at choice B.
Can you change that equation to make it look like the law of sines?

Answer 8

B.

\(a \cdot \sin B = b \cdot \sin A\)

What happens if you divide both sides by \(\sin A \sin B\) ?

Answer 9

cross multiply?

Answer 10

You can only cross multiply if you have a fraction equaling a fraction.
You need to do to choice B the opposite of cross multiply and end up with two fractions.
Do the division I mentioned above.
What do you get?

Answer 11

to be honest ! not really sure!

Answer 12

is the answer c?

Answer 13

This is still choice B.

Divide both sides by sin A sin B:

\(\dfrac{a \cdot \sin B}{\sin A \sin B} = \dfrac{b \cdot \sin A}{\sin A \sin B} \)

What cancels out of each side and what are you left with?

Answer 14

\(\dfrac{a \cdot \cancel{\sin B}}{\sin A \cancel{\sin B}} = \dfrac{b \cdot \cancel{\sin A}}{\cancel{\sin A} \sin B} \)

What is left?

\(\dfrac{a }{\sin A } = \dfrac{b }{\sin B} \)

Isn't what is left still the law of sines?
That means choice B. is not the answer.

Answer 15

Now work on choice C.
First, cross multiply.
Then divide both sides by sin B sin C.
What do you get?