Descriptive geometry . t of the angle between planes Nand i^, or its supplement. 86. Case 2. When it is required to deter-mine the angle between an inclined plane andeither coordinate plane. Construction. Figs. 133 and 134. Letit be required to determine the true size ofthe angle between planes iVand H. Pass theauxiliary plane JTperpendicular to both iVandH^ and, therefore, perpendicular to their line ofintersection, HN. Then HX and VX areperpendicular respectively to ffiV^and GrL. The angle between the lines ah and HX, inwhich plane X intersects planes N and H re- ANGLE BETWEEN PLANES 59 spec
Descriptive geometry . t of the angle between planes Nand i^, or its supplement. 86. Case 2. When it is required to deter-mine the angle between an inclined plane andeither coordinate plane. Construction. Figs. 133 and 134. Letit be required to determine the true size ofthe angle between planes iVand H. Pass theauxiliary plane JTperpendicular to both iVandH^ and, therefore, perpendicular to their line ofintersection, HN. Then HX and VX areperpendicular respectively to ffiV^and GrL. The angle between the lines ah and HX, inwhich plane X intersects planes N and H re- ANGLE BETWEEN PLANES 59 spectively, is the required angle, the true size mum inclination of plane iVwith H. of which, «, is determined by revolving the Suppose it is required to determine the true triangle containing it into F about FX as an size of the angle between planes iV and F. axis, or into ^ about HX as an axis. Determine the line of maximum inclination of The line ah is known as the line of maxi- plane N with F, and its angle with F. ^^. 60 DESCRIPTIVE GEOMETRY 87. To determine the bevels for the correctcuts, the lengths of hip and jack rafters, andthe bevels for the purlins for a hip roof. Fig. 135 represents an elevation and planof a common type of hip roof having a pitch equal to -—- and a width of ch. ah is the center line of the hip rafter ; ^ is a cross sec-tion of the ridge ; F^ K, Z, M, are jack rafters. Hip. To find the true length of the hiprafter eh^ and the following angles: Down cut, 1: The intersection of the hipwith the ridge. Heel cut, 2: The intersection of the hipwith the plate. Side cut, 3: Intersection of the hip withthe ridge. Top bevel of hip, 4. The true length of the hip eh may be ob-tained by revolving it parallel to V, as at e-J?^or parallel to H^ as at e^h^. The down cutbevel, 5, is obtained at the same time. Thebevel of the top edge of hip is found by pass-ing a plane perpendicular to ah intersecting the planes of the side and end roofs. HZ isthe horizontal trace of
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