Trigonometry lets you use some known quantities about a triangle to determine its unknown quantities, we will interrupt ourselves right now because we can already hear you muttering, “Come on, when am I ever gonna use this?” Here is when you are going to use this: in navigation, astronomy, music, number theory, engineering, electronics, physics, architecture, optics, statistics, cartography, and more. You already need it just to build a proper sundial, hence the unofficial slogan of trigonometry: “Okay, fine, I guess this is actually pretty important after all.” Trigonometry deals only with right triangles (triangles with two edges that meet at 90 degrees, and we mark that angle with a little square), but since any non-right triangle can be divided into two right triangles (try it; it’s true), that’s not going to be a problem.
“Trigonometry lets you use some known quantities about a triangle to determine its unknown quantities, we will interrupt ourselves right now because we can already hear you muttering, “Come on, when am I ever gonna use this?” Here is when you are going to use this: in navigation, astronomy, music, number theory, engineering, electronics, physics, architecture, optics, statistics, cartography, and more. You already need it just to build a proper sundial, hence the unofficial slogan of trigonometry: “Okay, fine, I guess this is actually pretty important after all.” Trigonometry deals only with right triangles (triangles with two edges that meet at 90 degrees, and we mark that angle with a little square), but since any non-right triangle can be divided into two right triangles (try it; it’s true), that’s not going to be a problem.”
— Ryan North · Science