# Construction Math

## Solving Unknown Lengths and Angles # III Dual Pitched Roof

Solving the Height ##### Known Values:
```Roof pitch no 1  = 9/12
Roof pitch no 2 =  5/12
length a = 20'
and from "Solving for length's aa and ab"
aa =  7' 1 11/16"
ab = 12' 10 5/16"
```
##### Solving the height from length ab plus the roof pitch
The rise for the length b side is 5" for every 12" of run
multiply length ab by the rise
12' 10 5/16 * 5
To be able to do this the units have to be the same. You could change the inches of the rise to the foot value by dividing by 12 and convert the ab length to decimal format but I find it easier to convert
12' 10 5/16 into decimal
12 = 12.0000
10 / 12 = 0.83333 (dividing by 12---12" equals one foot)
5 / 16 / 10 = 0.03125 (if you do not divide by 10 you end up with the value being a fraction of a foot)
= 12.86455 in decimal format
The 5" rise is in a run of 12" divide 12.86455 by 12
12.86455 by 12 = 1.0720458 multiply this by the rise of 5
1.0720458 * 5 = 5.36 (rounded to 2 digits)
The height of the truss = 5.36'
convert this to foot and inch
the 5 before the dot is the foot value subtract this from the amount
5.36 - 5 = 0.36
multiply the leftover decimal by 12 to remove the whole inches
0.36 * 12 = 4.32 the 4 before the dot is the inch value, subtract this from the decimal
4.32 - 4 = 0.32 Pick a denominator for your fraction. We will use 16.
Multiply the leftover decimal by 16 to get the numerator value of the fraction.
0.32 * 16 = 5.12 round this to the nearest whole number = 5 The numerator for the fraction will be a 5.

##### Collect the numbers:
The height of the truss is 5' 4 5/16"

### Height of Truss

Length ab ft in n
d
Roof Pitch / 12

#### Results:

 Height ft in