We are going to take this in two stages.
First I am going to introduce the formula which is written behind me and then I am going
to show you what each angle and what length refers to in which part of the triangle then
we are going to substitute drag and drop the formula and we are going to work out and come
up with the correct answer.
So let us start of stage no.
1.
Let me introduce to you what each part of the formulas are?
So let us have a look here, we are looking for the length little a, why?
Because it is opposite of capital A which is the angle 48 degrees so we are looking
for little a let me write it down here, right there, there is our little a, that is what
we are going for, and here is the formula looks like.
It is a squared = b squared + c squared – 2 bc cos A and now it is very long and lengthy
it is lot of characters and it is very long train and when we take the appropriate number
the correct numbers and put them in correctly it is all just drag and drop and it comes
up rather easy.
So let us start to look at and take a closer look at what each letter refers to here, what
each here what pro numeral refers to.
Well as I mentioned earlier little a refers to length directly in front of the 48 degrees
capital A now that is what we are looking here, right A that is what we are finding
over we got little b, and the little c where are they?
Capital B is down here so therefore directly opposite is will be little b so let me mark
that out there is our little b similarly right the opposite the capital C the angle is the
little c the length and we will call this little c right here.
Now that we have labeled our diagram our triangle displayed right over there we can easily see
where we can drag and drop the appropriate numbers so let us take another closer look
and continue with this very long formula.
Over here we continue with minus 2bc and then we multiplied is not in there it is actually
it is a dot by cos of the Alpha, in that Alpha or A that capital A is actually the capital
A angle right here 48 degrees.
Ok how do we know is cosine rule very easy it is cosine because it is cozy angle located
amongst two length we have the length C here 20 cm, and the length little b 17 cm so that
is how we diagnose and detect whether or not is it a cosine rule or another one.
So, these are the formula, let us start to drag and drop the appropriate numbers into
the formula.
So, let us start up, we have a squared equals – now we have little b which is right over
here that is 17 – 17 squared + then we have little c right there that will be 20 squared
minus 2 times.
Now, what is b again?
Little b is 17, yes, so we go 17 times little c, there is the little c there, put up there
– times 20 and then we cos alpha or A capital that is 48 degrees, let me put that in – we
write there – 48 degrees, there is a 48, there is a 48.
Okay, now, this 2 sections to this formula we are going to separate them in 2 sections;
the first section here is this part here, the 17 squared and 20 squared then we have
the other section here right there the second part of the trail or the second courage and
we are going to keep them separated until we finally subtract one from another because
as you can see, we have minus sign these.
So let us work out the section here – on the left first of all – so a squared is
equal to 17 squared in the calculator will yield 289 – plus 20 squared in the calculator
is 400 – minus let us go to the second part of the formula here.
Now we got 2 times 17 times 20 now on your calculator, just that part will yield you
680 – times cos and what is that cos 48 there is the cos 48, there it is there.
So we got the 2 section there, I am going further to simplify these section here in
the right – 680 times cos 48 on your calculator will give you a grand total of 455.
On the left hand side if we add up 289 plus 400 that is going to be 680 is in it?
689-455.
Okay, so a squared equals to that.
So let us subtract one from the other, 689-455 yields us on the calculator a grand total
of 234.
Now is that the length here 234 seems to be big, well do not forget it is an a squared,
we have to square root both sides so let us do that – square root, square root.
So eventually a is going to equal which is quote for bc it is a sine capital B, capital
C is the same as a, so that length right across there a square root of 234 is – 15.3cm.
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Take a minute to check out in our website at http://www.vividmaths.com.
You will find additional resources, cheat sheets, transcripts and other mass videos
that are not available in Youtube.
Lastly, don’t forget to subscribe to get access to all ready answer for all your math
questions plus other special offers.