Hip and Valley Sketches for 90 Degree Wall Angle

Hip and Valley Side Cut Angles
90° Angle in Plan between Hip Eaves or Valley Ridges

Common Pitch Angles and Plan Angles defined as per drawings
Hip -Valley Pitch Angle = 28.35605°

Hip -Valley Side Cut Angle: Hip Rafter Foot or Valley Rafter Peak:
arctan (cos Hip -Valley Pitch Angle × tan Plan Angle)
Hip -Valley Side Cut Angle: Hip Rafter Peak or Valley Rafter Foot:
arctan (cos Hip -Valley Pitch Angle ÷ tan Plan Angle)

Blade Bevel Angle along Hip -Valley Side Cut Angle:
arctan (tan Hip -Valley Pitch Angle × sin Hip -Valley Side Cut Angle)
Hip Roof: Plan and Sheathing Angles

Timber Valley Side Cut Angle Configurations
90° Angle in Plan between Valley Ridges

10/12 Main Common Pitch Angle = 39.80557°
13/12 Adjoining Common Pitch Angle = 47.29061°
Valley Pitch Angle = 33.44556°
Plan Angles defined as per drawings
Irregular Valley Roof Plan Angles

Irregular Valley Roof Equal Ridge Height Side Cut Angles

Sketch of Valley Peak intercepts 13/12 Ridge, Unequal 10/12 Ridge Height
Sketch of Irregular Valley Rafter intercepts 13/12 Ridge, Unequal 10/12 Ridge Height

Sketch of Irregular Valley Rafter intercepts 13/12 Ridge, Unequal 10/12 Ridge Height

Irregular Valley Roof Unequal Ridge Height Side Cut Angles

Gazebo Hip Rafter Side Cut Angles
135° Angle in Plan between Hip Eaves

8/12 Common Pitch Angle = 33.69007°
Plan Angle = 67.50000°
Hip Pitch Angle = 31.62973°
Gazebo Hip Rafters in Plan View