The hip rafter of a hipped roof

Lengths and Angles in Three Dimensions

At each of the four corners of a hipped roof, where two sloping planes run into each other, sits one timber: the hip rafter. To order it the carpenter looks at the roof plan, measures the line from the corner to the ridge and reads 5.66 m. The timber arrives at 5.66 m and it is short — the piece needed is 6.40 m. The plan was not drawn wrong; a plan simply cannot show a true length.