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
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
======return email munged================= take out the papers and the trash to reply
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
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.
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
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.
x-- 100 Proof News -
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?
ok. The phrases we had were:
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
Silly Old Horse Curly And Heavy Trod On Albert
does it for me :-)
errr...I'd better correct my typo before someone else does :-)
Should have been: .. Tea Pot Boiling = Tan(angle) = Perpendicular / Base.
0/10 See Me!Roger
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