Roof Angle Maths
 

Hi

I'm building a pergola for my sister in law and my grasp of maths is failing
me.

The roof is an isosceles triangle, e.g. two sides the same and a base.

The angle at the apex is 140 degrees and the two base angles 20 degrees. I
know the size of the base.

How do I calculate the length of the two identical sides and the height from
base to apex?

I seem to recall something about "some officers have, curly auburn hair,
till old age" but I think that only applies to a right angle triangle.

Dave

Hi David

On Wed, 20 Jul 2005 14:13:17 GMT, "David Lang"
wrote:

Hi

I'm building a pergola for my sister in law and my grasp of maths is failing
me.

The roof is an isosceles triangle, e.g. two sides the same and a base.

The angle at the apex is 140 degrees and the two base angles 20 degrees. I
know the size of the base.

How do I calculate the length of the two identical sides and the height from
base to apex?

I seem to recall something about "some officers have, curly auburn hair,
till old age" but I think that only applies to a right angle triangle.

Yup - you're right about the right-angled triangle - but your iso.
triangle can be seen as two right-angled triangles back to back....

The little jingle gives you sine, opp over hypot / cosine adjacent
over hypot and tan opp over adjacent....

So - if you plug in some figures

tan 20 = height / (base divided by 2)
sin 20 = height / long side

or - having got the height, derive the length of the long side by the
old squaw on the hippottamus theorem....

Hope this helps
Adrian

Dave


======return email munged=================
take out the papers and the trash to reply

On Wed, 20 Jul 2005 14:13:17 GMT, "David Lang"
wrote:

Hi

I'm building a pergola for my sister in law and my grasp of maths is failing
me.

The roof is an isosceles triangle, e.g. two sides the same and a base.

The angle at the apex is 140 degrees and the two base angles 20 degrees. I
know the size of the base.

How do I calculate the length of the two identical sides and the height from
base to apex?

I seem to recall something about "some officers have, curly auburn hair,
till old age" but I think that only applies to a right angle triangle.

Dave


Divide the triangle into 2 right angle triangles

You now have one side (1/2 the base), and all the angles.

So you look back as SOH CAH TOA

sin (angle) = length of side opposite angle / length of side next to
angle.

etc .........

Or you could reveal the length of the base, and some bright spake will
do this in their head for you.

Rick

"David Lang" wrote in message
...
Hi

I'm building a pergola for my sister in law and my grasp of maths is
failing
me.

The roof is an isosceles triangle, e.g. two sides the same and a base.

The angle at the apex is 140 degrees and the two base angles 20 degrees.
I
know the size of the base.

How do I calculate the length of the two identical sides and the height
from
base to apex?

I seem to recall something about "some officers have, curly auburn hair,
till old age" but I think that only applies to a right angle triangle.

Dave


Not totally with you on this Dave, but here goes with some sort of an
explanation. :-)

The angle at the apex is nearly a straight line when it's 140 degrees, so
you'll have to go a hell of a long length to reach the base with your beams
if you want a structure that average people can walk under.

What you need are vertical uprights which will support the roof at the
angles you want to make. So start by fixing uprights to the height of the
average person, say 2.1 mtrs, then build your roof on top of these at the
angles you say you need. You should then end with a structure that will
look pretty and be high enough to walk through without banging heads.

"David Lang" wrote in message
...
Hi

I'm building a pergola for my sister in law and my grasp of maths is
failing me.

The roof is an isosceles triangle, e.g. two sides the same and a base.

The angle at the apex is 140 degrees and the two base angles 20 degrees.
I know the size of the base.

How do I calculate the length of the two identical sides and the height
from base to apex?

I seem to recall something about "some officers have, curly auburn hair,
till old age" but I think that only applies to a right angle triangle.

If you drop a perpendicular down from the apex you have two right angled
triangles and can work from there.

If the base is 2B and half the base length is B, then

the vertical will be B x tangent(20deg)
the sloping edge will be B / cosine(20deg)

Bob Mannix

Hi Rick

Or you could reveal the length of the base, and some bright spake will
do this in their head for you.

Nah! Too easy! I just wanted my memory refreshed - it's all come flooding
back now!

The base is 72" which makes the height 13" and the roof sections 38" each
side.

Just after sizes for ordering enough materials.

Thanks to all who replied!

Dave

The only rhymn I know in that department is:

Some Old Hags... Sine(Theta) = Opposite / Hypotenuse

Carry A Huge... Cosine(Theta) = Adjacent / Hypotenuse

Tub Of Ale... Tan(Theta) = Opposite / Adjacent

Chris.


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In message , David Lang
writes
Hi

I'm building a pergola for my sister in law and my grasp of maths is failing
me.

The roof is an isosceles triangle, e.g. two sides the same and a base.

The angle at the apex is 140 degrees and the two base angles 20 degrees. I
know the size of the base.

How do I calculate the length of the two identical sides and the height from
base to apex?

I seem to recall something about "some officers have, curly auburn hair,
till old age" but I think that only applies to a right angle triangle.

Well, your roof is, in effect two right angled triangles, isn't it

with 20 degrees, 70 degrees and 90 degrees

but if you know the width and the height, then you need pythagarous

a^2 + b^2 = c^2

c^2 being the hypotenuse

--
geoff

raden wrote:
In message , David Lang
writes
Hi

I'm building a pergola for my sister in law and my grasp of maths is
failing me.

The roof is an isosceles triangle, e.g. two sides the same and a
base. The angle at the apex is 140 degrees and the two base angles 20
degrees. I know the size of the base.

How do I calculate the length of the two identical sides and the
height from base to apex?

I seem to recall something about "some officers have, curly auburn
hair, till old age" but I think that only applies to a right angle
triangle.
Well, your roof is, in effect two right angled triangles, isn't it

with 20 degrees, 70 degrees and 90 degrees

but if you know the width and the height, then you need pythagarous

a^2 + b^2 = c^2

c^2 being the hypotenuse

Nitpicky I know, but just to save a horrible over-ordering of timber, c is
the hypotenuse...


To get the height at the centre, split the roof (vertically) into two equal
right angled triangles

Then for each of these, the horizontal X is half the base width. You want to
know the length of the upslope Y, which goes up at a 20 degree angle.

Cos20 = X/Y so Y = X/cos 20 = X/0.94 = X * 1.06. Not all that much longer
really.

But in practical terms you need more than that for the roof to overhang.

And as another observation, 20 degrees seems like a very low pitch for a
roof, FWIW.


(Also, for this sort of job, I'd just draw it to scale and measure it
off...)

"PC Paul" wrote in message

And as another observation, 20 degrees seems like a very low pitch for a
roof, FWIW.

Fine for a pergola IME. Each roof 'panel' is roughly 40" x 40" so the area
isn't large. I judged the roof angle from several ready made pergolas I saw
in garden centres & sheds. Much more of an angle makes it look like a
rocket ship!

(Also, for this sort of job, I'd just draw it to scale and measure it
off...)

Exactly what I intend to do, now I have an idea of the sizes I'll order the
material.

Thanks all.

Dave

David Lang wrote:

Hi

I'm building a pergola for my sister in law and my grasp of maths is failing
me.

The roof is an isosceles triangle, e.g. two sides the same and a base.

The angle at the apex is 140 degrees and the two base angles 20 degrees. I
know the size of the base.

How do I calculate the length of the two identical sides and the height from
base to apex?

I seem to recall something about "some officers have, curly auburn hair,
till old age" but I think that only applies to a right angle triangle.

Dave


An isocelese triangle is two right angled ones stuck together, conceptually.

YOU work it out.

I can't work out how a single triangle can actually form a roof at all...

The Natural Philosopher wrote:
David Lang wrote:

Hi

I'm building a pergola for my sister in law and my grasp of maths is
failing me.

The roof is an isosceles triangle, e.g. two sides the same and a
base. The angle at the apex is 140 degrees and the two base angles 20
degrees. I know the size of the base.

How do I calculate the length of the two identical sides and the
height from base to apex?

I seem to recall something about "some officers have, curly auburn
hair, till old age" but I think that only applies to a right angle
triangle. Dave


An isocelese triangle is two right angled ones stuck together,
conceptually.
YOU work it out.

I can't work out how a single triangle can actually form a roof at
all...

Never seen a lean to?

In message , PC Paul
writes
raden wrote:
In message , David Lang
writes
Hi

I'm building a pergola for my sister in law and my grasp of maths is
failing me.

The roof is an isosceles triangle, e.g. two sides the same and a
base. The angle at the apex is 140 degrees and the two base angles 20
degrees. I know the size of the base.

How do I calculate the length of the two identical sides and the
height from base to apex?

I seem to recall something about "some officers have, curly auburn
hair, till old age" but I think that only applies to a right angle
triangle.
Well, your roof is, in effect two right angled triangles, isn't it

with 20 degrees, 70 degrees and 90 degrees

but if you know the width and the height, then you need pythagarous

a^2 + b^2 = c^2

c^2 being the hypotenuse

Nitpicky I know, but just to save a horrible over-ordering of timber, c is
the hypotenuse...

Bugger ... you know what I meant, I blame the Chimay




To get the height at the centre, split the roof (vertically) into two equal
right angled triangles

Then for each of these, the horizontal X is half the base width. You want to
know the length of the upslope Y, which goes up at a 20 degree angle.

Cos20 = X/Y so Y = X/cos 20 = X/0.94 = X * 1.06. Not all that much longer
really.

But in practical terms you need more than that for the roof to overhang.

And as another observation, 20 degrees seems like a very low pitch for a
roof, FWIW.


(Also, for this sort of job, I'd just draw it to scale and measure it
off...)



--
geoff

"Chris McBrien" wrote in message
. ..
The only rhymn I know in that department is:

Some Old Hags... Sine(Theta) = Opposite / Hypotenuse

Carry A Huge... Cosine(Theta) = Adjacent / Hypotenuse

Tub Of Ale... Tan(Theta) = Opposite / Adjacent

ok.
The phrases we had we

Suet Pudding Hot = Sine(angle) =Perpendicular / Hypotenuse.

Cold Boiled Ham = Cos(angle) = Base / Hypotenuse

Tea Pot Boiling = Tan(angle) = Perpendicular / Hypotenuse

Where angle = the included angle in degrees.
(We also used to call this Theta)
Apart from the different synonyms our phrases viewed the triangle as
'upright', that is with the right angle at one of the lower corners,
whereas your rhymns enable the user to imagine the triangle in any
orientation.

Roger

errr...I'd better correct my typo before someone else does :-)

Tea Pot Boiling = Tan(angle) = Perpendicular / Hypotenuse
Should have been:
... Tea Pot Boiling = Tan(angle) = Perpendicular / Base.

0/10 See Me!

Roger