unit length unit rise ratio

hi im doing some triginometry right now and have got used to what i need, tangents secants etc but im having a problem with one thing, im not sure if my question wont be very easy for one of you, i hope so! , and hopefully youll enjoy working it out but im getting a mental block so it needs asking as its holding me back working other things out in my equations.

ok so im studying some books on roofing for framing regular and complicated irregular roofs but all the best literature on the subject is from usa, where they use a different system, they work in feet and inches so when they ratio a roof they have a base unit of 12, i am trying to make my own system by translation

thus a roof there would be described as a 4in12 pitch roof or 8in12 or 12in12 which is a 1/2 pitch, meaning it rises 12 inches for every 12 it runs, here we work to roof degrees, so i need my rise to be measured per metre! such as 300mm rise per 1metre or (1000mm)

so my question is this, if i have a right angle triangle for example with a rise or 600mm/a run (or adjacent side) of 848mm/ making the hypotenuse a total length of 1039........can you tell me what my unit length would be or put another way......what is my rise (600) per metre if 848 is my length?

simple equation would be nice too so i can use it on other numbers as my base, thanks (for visualization this triangle is 35degrees angle) imagine half a roof..

so once again im looking at finding my 'rise per metre' (unit rise) from any of the other available data i have, inc. deg tan sec total rise, total run, and rafter length (hypotenuse) i know its some sort of 10 calculation but its weighing my brain, thanks again

(another example for a 45deg roof, unit rise would be 1000mm for every 1000mm or300mm in every 300mm, but for a roof of 42.5 degrees if rise was 275mm in every 300mm run, what would per metre(1000mm) rise be?

Re: unit length unit rise ratio

if you have any angle of pitch = $\displaystyle \theta$, then $\displaystyle \tan{\theta} = \frac{rise}{run} = \frac{y}{1000}$

$\displaystyle y$ is the rise per meter (1000 mm) , and can be calculated

$\displaystyle y = 1000\tan{\theta}$

for example, for a 42.5 degree pitch, $\displaystyle y = 1000\tan(42.5^\circ) \approx 916.33 \, mm$

Re: unit length unit rise ratio

id love to be able to read what you just wrote but im not a mathemetician it looks a little bit like greek, thanks anyway for trying

Re: unit length unit rise ratio

Quote:

Originally Posted by

**pza** id love to be able to read what you just wrote but im not a mathemetician it looks a little bit like greek, thanks anyway for trying

if you just want to convert the ratio ...

$\displaystyle \frac{rise}{1000} = \frac{275}{300}$

$\displaystyle rise \, = 1000 \times \frac{275}{300}$

Re: unit length unit rise ratio

you lost me again!

so one last time if i have a rise of 600 and run of 848..........what is my unit rise per 1000&how?

thanks.

Re: unit length unit rise ratio

Quote:

Originally Posted by

**pza** you lost me again!

so one last time if i have a rise of 600 and run of 848..........what is my unit rise per 1000&how?

thanks.

you are working with equal ratios ...

600 is to 848 as $\displaystyle y$ (the rise you want) is to 1000

$\displaystyle \frac{y}{1000} = \frac{600}{848}$

$\displaystyle y = 1000 \times \frac{600}{848} \approx 708 \, mm$

Re: unit length unit rise ratio

ive got it!

thanks for walking me through it till i grasped it (Handshake)

(my framing square was confusing me but i had worked out a sum too many)

thanks again!