## tw101 one year ago Using the law of sines, in triangle ABC, if m<C=135, M<B=10, c=45, find measure of a

1. tw101

@LegendarySadist I know you already helped me with one like this, but this one is a bit different. How do I solve when it has all three variables?

2. anonymous

So |dw:1436210371264:dw|

3. tw101

i have it set up like: sin(a)/a=10/b=135/45

4. anonymous

Oh, we're looking for a|dw:1436210449197:dw|

5. anonymous

When we look for side lengths, it's easier to put the side lengths on top. So $\large \frac{a}{sin(35)}~=~\frac{45}{sin(135)}$

6. tw101

7. anonymous

I thought that's what we were solving for at first, but since we're not we can ignore it.

8. tw101

oooh okay so its just extra information?

9. anonymous

Well the m<B allowed us to find m<A so not really. Me putting in "b" was extra info though.

10. tw101

okay. so just solve the equation above?

11. anonymous

Yep :)

12. tw101

and like the last one multiply both sides by 35 to get a alone?

13. anonymous

Well sin(35), but yes

14. tw101

okay one second

15. tw101

I got .900

16. anonymous

That's not what I got /:

17. anonymous

$\large a~=~\frac{45 \times sin(35)}{sin(135)}$

18. tw101

19. anonymous

That's closer, but not exactly it

20. tw101

i put: sin -1 (35*sin(1350/45 into my calculator

21. anonymous

There's the problem. We're solving for a, not sina. So no need for asin.

22. tw101

that was my answer when i put that into the calculator

23. tw101

OOOH

24. tw101

okay wait so im confused now when i multiply both sides by sin 35 is that it?

25. anonymous

$\rm \large a~=~\frac{45 \times sin(35)}{sin(135)}$

26. tw101

36.50?

27. anonymous

Correct!

28. tw101

whew! finally haha thank you again youre a lifesaver!

29. anonymous

$\huge \color{aqua}N\color{fuchsia}o \space \color{lime}P \color{orange}r \color{blue}o \color{maroon}b \color{red}l \color{olive}e \color{purple}m \ddot\smile$