Using the law of sines, in triangle ABC, if m

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Using the law of sines, in triangle ABC, if m

Mathematics
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@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?
So |dw:1436210371264:dw|
i have it set up like: sin(a)/a=10/b=135/45

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Other answers:

Oh, we're looking for a|dw:1436210449197:dw|
When we look for side lengths, it's easier to put the side lengths on top. So \[\large \frac{a}{sin(35)}~=~\frac{45}{sin(135)}\]
What about B?
I thought that's what we were solving for at first, but since we're not we can ignore it.
oooh okay so its just extra information?
Well the m
okay. so just solve the equation above?
Yep :)
and like the last one multiply both sides by 35 to get a alone?
Well sin(35), but yes
okay one second
I got .900
That's not what I got /:
\[\large a~=~\frac{45 \times sin(35)}{sin(135)}\]
wait what about 33.36?
That's closer, but not exactly it
i put: sin -1 (35*sin(1350/45 into my calculator
There's the problem. We're solving for a, not sina. So no need for asin.
that was my answer when i put that into the calculator
OOOH
okay wait so im confused now when i multiply both sides by sin 35 is that it?
\[\rm \large a~=~\frac{45 \times sin(35)}{sin(135)}\]
36.50?
Correct!
whew! finally haha thank you again youre a lifesaver!
\[\huge \color{aqua}N\color{fuchsia}o \space \color{lime}P \color{orange}r \color{blue}o \color{maroon}b \color{red}l \color{olive}e \color{purple}m \ddot\smile \]

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