The Crystal Palace pane of glass (49 inches) as the hypotenuse of a right-angled triangle, thereby creating a triangle with a length-to-height ratio of 2.5:1, whose base (adjacent side) was 4 feet long. By mirroring this triangle he obtained the 8-foot-wide gables that formed the vertical faces at either end of the prism, each of which was 24' long. With this arrangement, Paxton could glaze the entire roof surface with identical panes that did not need to be trimmed. Paxton placed three of these 8' x 24' roof units side-by-side, horizontally supported by a grid of cast iron beams, which was held up
Altitude (triangle) the tangential triangle, and the center of similitude of the orthic and tangential triangles, are on the Euler line. Trilinear coordinates for the vertices of the tangential triangle are given by For more information on the orthic triangle, see here. For any triangle with sides and semiperimeter , the altitude from side is given by This follows from combining Heron's formula for the area of a triangle in terms of the sides with the area formula (1/2)×base×height, where the base is taken as side and the height is the altitude from . Consider an arbitrary triangle with sides and with