Trigonometry is particularly significant in architecture because it enables the architect to calculate distances and forces associated with diagonal features such as roofs and bespoke ceilings. These calculations are useful for designing efficient spaces that use materials effectively and minimize waste. For example, if an arch has a radius of 10 feet, then it will have an opening width of 5 feet. This means that you can only pass two-foot-wide objects through the arch. If something larger is needed, then it will have to be split into two or more pieces. The same thing applies to doors. If a door is 10 feet wide, then it will close only 3 feet instead of 4 feet. This means that you lose space that could otherwise be used as storage or work area. In buildings, diagonals are important elements in design. They provide stability against earthquakes and wind pressure. They reduce noise by allowing air to flow through the building and by providing shade from the sun for interior offices or apartments. And they add beauty to the structure. Modern architects often include geometric shapes in their designs as a source of tension or stress to which the building responds by forming beautiful structures that fulfill functional requirements as well.