Let me write out this right angle here because we are looking for one these side lengths
and we are given hypotenuse.
So Pythagoras theorem looks like this as we know – a squared + b squared = c squared.
Now c squared here c refers to the hypotenuse now in this particular instance it is already
given so we can now actually put the number in there, so we can just go in inside.
Well that is going to be 75 – so let us put that in – squared.
now one of the sides is already given to which is 62 right across this so let us put that
in – so that is 62 squared.
now a or the other length right here connected to the right angle is just we call it X as
it is write in there so let us just write down X squared – so the theorem and the
equation looks like these – X squared + 62 squared they are the two length connected
to the right angle, X squared + 62 squared = the hypotenuse all the way across there
that very long length 75 squared.
Now remember what I said earlier?
We subtract whenever we are given the hypotenuse and we are looking for one of the side length.
So what does that mean?
It means we are going to get something like this—x squared = and then we take away this
and bring it over to that side and then it becomes 75 squared – 62 squared so let us
subtract that from both sides so I will just go minus 62 all squared and then minus 62
all squared on that side too so then quite simply this drags down over here and this
cancel so let us work with this side here we will get 75 all squared minus --- 62 all
squared so as I said earlier I will just recap when we are given hypotenuse across there
it is the hypotenuse one of the side length which is that one across there so now we can
solve we can see one of the subtraction there.
So it is going to be x squared = well on the calculator 75 squared is going to be let me
just check on that, that is just 5625-- take away 62 all squared let me check on that,
that is 3844, 3844 ok put that into your calculator and we will end up with x squared = 5625 – 3844
will give us 1781 so let us write that in so 1781 now remember it is x squared so we
need to square root both side so let us do that, so let us square root the left hand
side and we square root the right hand side that is right like that, so the squared root
of s squared will revert to just a normal X, so X = and that is the length across here
that we are looking for and the square root of 1781 is 42.20m.
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