The situation is especially nice for right triangles, because then we only have five unknown features since one of the angles is \frac{\pi}{2} radians (or 90^\circ), as demonstrated in Figure. If we know one of the two non-right angles,
- then we know the other as well. Moreover, if we know any two sides, we can immediately deduce the third, because of the Pythagorean Theorem. As we saw in Preview Activity, the cosine and sine functions offer additional help in determining missing information in right triangles. Indeed, while the functions \cos(t) and \sin(t) have many important applications in modeling periodic phenomena such as osciallating masses on springs, they also find powerful application in settings involving right triangles, such as in navigation and surveying.
+ then we know the other as well. Moreover, if we know any two sides, we can immediately deduce the third, because of the Pythagorean Theorem. As we saw in Preview Activity, the cosine and sine functions offer additional help in determining missing information in right triangles. Indeed, while the functions \cos(t) and \sin(t) have many important applications in modeling periodic phenomena such as oscillating masses on springs, they also find powerful application in settings involving right triangles, such as in navigation and surveying.