## anonymous one year ago Which of the following cannot be derived from the law of sines?

1. anonymous

2. Loser66

What is the law of sines?

3. anonymous

dont know.... lol that why i asked

4. Loser66

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?

5. anonymous

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

6. mathstudent55

Law of Sines $$\large \dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$$

7. mathstudent55

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.

8. mathstudent55

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

9. mathstudent55

B. $$a \cdot \sin B = b \cdot \sin A$$ What happens if you divide both sides by $$\sin A \sin B$$ ?

10. anonymous

cross multiply?

11. mathstudent55

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?

12. anonymous

to be honest ! not really sure!

13. anonymous

14. mathstudent55

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?

15. mathstudent55

$$\dfrac{a \cdot \cancel{\sin B}}{\sin A \cancel{\sin B}} = \dfrac{b \cdot \cancel{\sin A}}{\cancel{\sin A} \sin B}$$ 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.

16. mathstudent55

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