Hi guys.
They say that 2 is company and 3 is a crowd, and this triangle here is crowded with 3 pieces
of information because we are looking at 1 piece of information and that is the missing
pronumeral here it is here, the little c. the length across there, the distance is what
we are looking for.
So what are the 3 pieces of information that we do have?
Well first of all we have the big B here is which is the angle 47 degrees and opposite
that is the length or distance which is 5.8kms and up here the other piece of information,
the final piece, is 68 degrees that is big capital C opposite the little c pro numeral
that we are looking for.
We are going to use sine rule , we are going to substitute into this formula and then we
are going to cross multiply and we are going to shoot through in to the solution which
is little c the pro numeral.
So let us put the numbers into the formula here.
So it is already been labeled here in the triangle.
So we have got little b which is opposite big B right there so let us start up with
this part of the formula right here.
Can you see that little b right there, let us put that there, so little b is 5.8 kms,
so there it is there we are substituting it in there.
So we have – all over sinB which is going to be sine capital B and you can see what
that is – sine capital B up across there is 47 degrees that goes there which is right
over here.
And that equals little c over sin big C, let us write down the little c – right there
all over – sine 68 that is the big C right there, the
angle let us put that in there – okay, there it is.
Let us point out one more time to ensure we are correct.
So we got little b on big B, sinB there is little b, little b, opposite right there let
me just draw a line so we can see it, there and there is another line that goes across
there.
So double checking 5.8 over sin47 equals little c, there is the little c opposite 68 so sin68
right there so let us cross multiply so we can come up with it.
So it is going to be c times sin47 degrees and that equals this way, we have – (5.8
times sin68 degrees) okay, there is our equation we want to get c by itself, the pronumeral
so we can find the solution so that is the guard we want by itself and we want as the
subject to this equation.
So let us divide both sides by sin47 so we can eliminate that there right.
So we divide by sin47, divide by sin47 – so therefore this part here it cancels, so cancel
that, cancel that, because sin47 divide by sin47 is 1 as you already know.
So we are left with 5.8 times sin68 on sin47 and that is what c equals right – c equals
that – okay let us put that in to the calculator directly– 5.8 times sin68 divided by sin47
then press equals.
So our c equals, once we put that in and the answer will be in km, it is the length right
across there, there is our little c that equals – 7.35km.
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