Hi guys have you ever heard the rules never sign unless you read the fine print?
Well that is really interesting because we are doing the sine rule and in the question
there is a lot of fine print and we are going to check out and let me read it to you the
fine print says this, it says find the angle theta if it is obtuse?
In fine print that means that this is the angle that looking for theta right around
here and you might notice that it thus is looks obtuse, and obtuse meaning as you all
know greater than 90 degrees that look kind a big, thus in it?
So that is what we are looking for so there is a little trick in this, and I am going
to walk you through it and you are going to see exactly what to do when you got a question
like this now this is one of the tougher question but at the same time we are going to learn
how to do find angles instead of length using the sine rule.
So let us get into the details of this, this is the sine rule formula equation whatever
you want to call it.
and I am going to give you a quick short cut on how to do this without having to refer
to the sine rule all the time.
Since we know that it is all about cross multiplication, what we are going to do is go angle and distance,
angle and distance and put distance over the angle that is all we do in cross multiply.
Let us do that now, so let us start off with distance over angle let us do that—distance
over sign of the angle which equals distance over sign of the angle –
ok there we have the basic equation let us do normally we do in with the sine rule that
is to cross multiply let us do that.
So first of all we are going to get – this corner x that corner – that corner x that
corner—ok what do we after now?
What we are after the angle theta right over here so that means we want to isolate and
make singular this theta right there so let me just underline that because that is what
we are looking for, right there.
So what we are going to do?
We divide both sides by 100 to get rid of that 100 to make this part by itself so let
us do that – so that is going to give us –
there we go, so theta = 210 x sin 26 all over 100.
Let us put that in the calculator, so 210 x sin 16 / 100 gives us – ok sine theta
0.9206 we are after theta by itself so let us shift sin now, we shift sin that will give
us 67 degrees zero minutes 40 seconds remember just before we got that answer we also presst
shift DMS or degrees minutes seconds and yields 67 degrees zero minutes 40 seconds that can
be rounded up into 67 degrees 1 minutes, because the 40 that is above 30 let us do that let
us write that over here sot the answer we have for theta is 67 degrees 1 minute –
ok that is what we have now but it is not obtuse remember the fine print, read the fine
print in the question.
So we want to check this out 67 0 1, what do we do?
how do we make it obtuse?
That angle thus look obtuse it thus looks bigger than 90 degrees so what we do quiet
simply is take it away from 180 degrees that will make it obtuse let us do that.
Let us go take away the 67 0 1, -- and that is going to gives a total 67 0 1 is that going
to give us the angle – on your calculator 180 – 67 0 1, the angle right in here is
theta in -- 112 degrees 59 minutes.
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