Let us do the first step which is we are going to label this and then we are going to get
back to this formula I am going to show you a short cut on how you can actually substitute
drag and drop the numbers from there into there. So let us label and identify so what
we have here? well clearly we have 3 sides as I mentioned earlier so opposite the big
B which is the angle we have little be right over here so that goes across there and opposite
the angle big C we have the length C right over there so that goes up that way and clearly
the angle A right opposite that whole length that whole side is refer to little a. ok we
know the a, b, c, are now we are going to take this guys drag and drop them into this
formula here. Now we are looking for the angle so later on we are going to do a shift or
inverse cos of the angle so we can find out the exact angle in degrees and minutes.
So taking the information from here going across here, we have got the formula up here
now you might notice in this formula that we have a squared and c squared here and what
thus that means? It means that the two length that are between and cosie with the angle
are the two length a & c right here. so you will notice next to capital B which is the
angle we have c & a, we have c & a and the opposite length right here the B is equivalent
to the angle we are looking for right on the other side were we subtract so there is that
b right there and it is usually the opposite were we subtract that in the formula.
So let us take these guys and put them in the formula now, yeah? so we have cos B which
is what we are looking for – and we have a squared and c squared. a squared we have
7 squared, yeah? -- + c squared right up there that is the 6 – minus b squared and the
b is across here right there we have a 9—9 squared all over 2 x a x c which is 2 x we
have an a that is the little a right there 7 x c we look at little c right there that
is 6 – ok all we got to do is put that in to the calculator. 7 squared + 6 squared for
all we know that is going to be 49 + 36 – 81. Hopefully we have a small number on the top
and a bigger number on the bottom because we want to get the decimal that is O. something.
2 x 7 x 6 will give us 84 that is cos B again.-- now as we simplify this 49 + 36 take away
81 on the calculator will give you a grand total of 4-- 4/84 let us do that 4 /84 will
give us a decimal and that is going to give us 4 /84 is 0.0476. ok now we are looking
for – cos B specifically the B that is 0.0476 now let us go with the calculator and shift
or 2nd function 0.0476 and that will give us an angle B which = on the calculator the
angle right there which is what we are looking for angle B = 87.27 now we can get more specifically
to that and we can change it in degrees minutes seconds and then we go shift or 2nd function
DMS ( degrees minutes seconds) = and our final answer for that angle there will be – B
= 87 degrees and 16 minutes on your calculator.
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