Construction Math

Solving Unknown Lengths and Angles # IV Dual Pitched Roof

Solving the Angles

A dual pitched roof has the shape of a scalene triangle and as with all triangles, the combined three angles add up to 180 ° . From the two roof pitches you will be able to get the angles B and C.

Using the same known values as before:

Roof pitch no 1  = 9/12
Roof pitch no 2 =  5/12
length a = 20'

Solving for angle B

Using the inverse Tan function for a 9/12 pitch. Divide the rise by the run

9/12 = 0.75
Arctan (0.75) = 36.8699 °     B = 36.9 °  (rounded to 1 digit)
Angle  B = 36.9 °

Solving for angle C

Using the inverse Tan function for a 5/12 pitch. Divide the rise by the run

9/12 = 0.416667
Arctan (0.41666667)   = 22.6199 °   C = 22.6 °  (rounded to 1 digit)
Angle C = 22.6 ° 

Solving for angle A

All the corners of the triangle have to add up to 180 °

180 - 36.9(B) - 22.6(C) = 120.5 ° .
Angle A = 120.5 ° 

Solving for angle ab

db = 90 °  and B = 36.9 ° 
ab = 180 - 90(db) - 36.9(B) = 53.1° 
Angle ab = 53.1°

Solving for angle ac:

A = 120.5 °  
ab = 53.1° 
ac = 120.5 - 53.1 = 67.4 ° 
Angle ac = 67.4 ° 

• Construction Math - Index
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• Equation Manipulation
• Calculating with Percentages
• Square Footage of a Rectangle Calculator

Solving a Duel Pitch

1. What can you do with the roof pitch?
2. Solving for length's aa and ab
3. Calculating the Height
4. Solving the Angles