## 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 °

### Angle of Roof From Roof Pitch