Capítulo X · Neste capítulo você vai
Any triangles
- demonstrate the law of cosines and the law of sines;
- calculate the area of a triangle from two sides and the angle between them, the three sides (Heron’s formula) or the radius of the circumscribed circle;
- calculate heights, medians, angle bisectors and the radii of the circles inscribed and circled from the sides;
- solve any triangle in the four classical cases, including the ambiguous case.
In the previous chapter, the right angle did all the work: with it, the sine, cosine and tangent of an acute angle were enough. In any triangle there is no right angle at hand, but there are two laws that take their place. The law of cosines generalizes the Pythagorean theorem; the law of sines connects each side to the opposite angle and the circumscribed circle. With them, any triangle can be solved.