Hi guys, I am presenting in this example the perfect pitch for this roof.
What is that perfect pitch?
Well if you look over here, we have a kind of a house thing happening here right and
we have width the house across here which is 10.6 and right down in the middle because
the picture of the roof is an isosceles triangle which means this side and other side is equal
which also means that the base and angles are the same.
We are going to work with one side, don’t need to work for both; we are going to work
on this over here.
Now here are the question asks, it says find the pitch of the roof, what is the pitch of
the roof?
The pitch is in this angle here, it’s from the horizontal up right?
From the horizontal up is the pitch of the roof that we are asked to find.
Now there are some interesting information in here and some clues that we can find from
the question and what we are going to notice is the width of the whole house and the width
of the roof of 10.6, that’s not good to us because we just want the triangle in here,
we pick one right handed triangle, it’s going to be right angle triangle because it
can’t work it out anyway.
This are a right angle, this are pitch, look at the height it’s 4.9, however the width
10.6 goes all the way cross over it goes over this little triangle over here so we are going
to find the section there.
So the first step we are going to find, what the half roof so we can get the area.
Then we are going to find what kind of ratio it is a sign or a cos or a tan and then we
are going to plug it in and get inverse shift whatever trig rusher is and we can come up
with an answer, we need to get it into the nearest minute which means we are going to
decide up or down.
So let’s go through it.
First things first, let’s find how wide it is right here.
Now if it is a perfect pitch to a roof?
And that is an isosceles triangle clearly that means straight down in the middle we
can cut that 10.6 in half, so the half of 10.6 is what?
– it is 5.3 so let’s mark that in its 5.3. so this part here across here is 5.3
so now we have a beautiful right angle triangle so now we can work with this triangle stuff.
Ok let us get to the ratio, the ratio will going to be thither this thither right over
there – equals.
Now let’s take closer look and see which sine, cos, or tan is in fact so if I was to
draw arrows here, I would look straight opposite here, right across there we got the 4.9 so
got the opposite thing happening.
And then right next right down the bottom here where the pitch of the horizontal roof
is right there we have the 5.3 that is called what?
adj – adj.
adjacent – so it is opposite over adjacent, okay what is opposite over adjacent?
It is - tan – you know that tan thither opposite adjacent so let’s put in the number.
So opposite right in front of here so it’s 4.9 and then right across here in red is that
5.3 – okay, let’s bring our tan thither over down – now on the calculator 4.9 divided
by 5.3 is 0.9243 let’s go to at least 4 decimal places to be more accurate.
Okay, let’s bring down the tan thither again, now we want to inverse tan we are going to
bring it down so we are going to bring thither make it by itself individual, make it single.
Let us bring down thither equals tan shift into inverse of that – let’s write it
down again 0.9243 – okay, when we put that in calculator shift tan 0.9243 gives us in
the decimal degree and it will be 42.7543 degrees.
Now all we have to do is transform it, shift it, change it into degrees, minutes and second.
So thither is going to equal to put it in shift dms or shift degrees minute and seconds
and that’s going to yield 42 degrees 45 minutes and 15 seconds.
Now have a look at this 15 seconds is it below or above 30 it is below which mean what do
we do with the minutes?
We leave them as they are do not we so?
Final answer the pitch the angle over there the right for this angle and the isosceles
on the other side that there in green is 42 degrees 45.
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