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...)