This time we are looking for an angle in this particular example, and the angle is the angle
C down here or you co-call CAB that is what we are looking for, let us have a look at
the formula it is the same as before except the C the angle is in the subject on the left
hand side. So we have cos C the angle right over here that we are looking for = a squared
+ b squared – c squared all over 2ab. Now it is fantastic news to get 3 sides no angle
because there is no other rule you can use, the only tool you can use, the only technique
is cosine rule and this is it here. So let us do the first step and label on the diagram
displayed right over here and then substitute into the formula and then come up with the
angle C so let us take in the first step.
So the first step is to label, so let us have a look here, we are looking the angle C down
here and directly opposite right up there is the little c that is the length and that
is 4. Now over here capital A which is the angle opposite to 5 and again the 7 that is
going to be little b opposite the big angle capital B and remember down here is going
to be little a. so we got all the little a’s and b’s labeled on there we have the angle
already labeled all we got to do is drag and drop that into the formula the cos rule formula
for the angle C. now let us put the values in – so first of we have cos C – which
is what we are looking for and that = a squared, let us go to a squared that is down here as
5, we label a=5, let us put that in 5 squared + little b let us have a look goes from big
B to little b that is going to be 7, yeah. minus directly opposite the angle we are looking
for directly opposite that length there is 4 so that is going to be 4 squared –as the
formula indicates now underneath we have 2 x a b so that is going to be 2 x 5 x 7 ok,
that is all the value from there substitute it into the formula let us work that out.
So cos C = 5 squared + 7 squared – 4 squared all in the calculator that will give you a
grand total of –58 all over 2 x 5 x 7 that is going to give us 70. Ok, so cos C = 58/70
you know it is going to be a decimal; it is going to be – 0.8286. Now cos C = that,
what do we do get the angle? We are going to shift cos on both sides we shift cos here
we will left with just with the C – so shift cos 0.8286 gives us an angle of – 34 degrees
and 3 minutes press shift DMS shift degrees minutes seconds.
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