Spike's Calculators

# 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 °
```

### Angle of Roof From Roof Pitch

Roof Pitch /12
Decimal Precision #