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#1
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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 |
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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 |
#3
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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 |
#4
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"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. |
#5
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"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 |
#6
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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 |
#7
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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 - http://www.100ProofNews.com x-- 30+ Days Binary Retention with High Completion x-- Access to over 1.9 Terabytes per Day - $8.95/Month x-- UNLIMITED DOWNLOAD |
#8
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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 |
#9
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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...) |
#10
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"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 |
#11
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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... |
#12
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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? |
#13
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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 |
#14
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"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 |
#15
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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 |
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