Hi guys over here to my left to your right we have an excellent triangle we are going
to work out the area of it. it is the triangle a, b, c . now that internal area is what we
are going for, we want the total area the unit are in centimeters and the first thing
we are going to do is to write up the formula and you remember the formula for the area
of the triangle. The area of a triangle is A = ½ x b x h, so what is the base for this
one? The base is 8cm and the height for this one as you can see it does not have a height?
Maybe we just measure the height anyway we just measure it or we cannot do that because
if they have not given as the height then clearly we cannot use it, so ½ x b x h actually
I just remember and you might noticed that, that formula is for what kind of triangle?
It is for a – right angle triangle, yeah. When you have a right angle triangle that
is the right angle triangle 90 degrees you cannot use that formula-- for a non-right
angel triangle so this is a non-angle triangle we are given an angle and two length between
it this angle kind a cozy in there and there is a new formula and I wonder if I can remember
that new formula nit goes something like year of a non-angle triangle. non-angle triangle
here we are none angle triangle area. I am going to give you that formula now it is a
fabulous formula it is a new tool that we can use to find areas without a need that
formula. It is here we are – A=1/2 that is look familiar
AB sine C so if the angle would given this C, the two link in between is the angle we
go for. In this particular instance, in this particular example you pause to modify this
formula that I just pick out of the book and modify it to suit this particular triangle
angel the formula would go something like this as A= ½ now we are going to put in links
so we can identify who they are because link are opposite the capital letters, remember
what did before so if we are going to the capital B here little “b” is there, if
we have capital A there which is the angle length across here is little “a” and also
if we got the angle there C opposite here the length will our little “c” so the
rule opposites and if we are to put them in this triangle here then we would have something
like this it will be a ½ x the two now the two ones on the side as you can see the c
and a, so start with a and c so it will be a x c x sine and the angle which is the capital
right over here angle C that? That is b, so that is our new formula that is what we are
going for. Ok so, let us take the values from here substitute
them in there and we will be able to work out the whole are of a, b, c triangle. So
let us do that, so the area would be A= ½ x ac, here is little a right there 8cm x little
c which is 7 and then we finish of with sine the angle that we have given there what is
that? That is 30 degrees, excellent there is our formula all substitute it in there
and a rule a thumb to make it nice and short and easy next time you do this is the angle
goes right there whatever angle and the two side right between is there and there the
8 and the 7 yeah. So let us finishes this off, so A=1/2 x 8x7 is 56 and then sine 30
in the calculator is ½ or .5 , so a ½ x 56 x ½ now a ½ of 56 is 28, ½ of 28 is
14. So the total area right here --- of the whole triangle a, b, c—A=14cm squared, do
not forget the cm squared because it is a area.
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