Resoluci\'on de tri\'angulos oblicu\'angulos

TL;DR

This paper presents the main theorems for solving oblique triangles, illustrating five classical and some atypical cases, and discusses related calculations such as area, radii, and segment lengths.

Contribution

It introduces a comprehensive approach to solving various oblique triangle cases, including atypical scenarios, with detailed methods for related geometric calculations.

Findings

Solved five classical cases of oblique triangles

Analyzed atypical cases with known perimeter and angles

Derived formulas for area, radii, and segment lengths

Abstract

Se enuncia los principales teoremas empleados en la resoluci'on de tri'angulos oblicu'angulos. Con ellos, se ilustra c'omo resolver los cinco casos de resoluci'on que se presentan, incluyendo algunos caso at'ipicos (cuando se conoce el per'imetro y dos 'angulos internos, o un lado, el 'angulo comprendido entre los lados restantes, as'i como su suma). Luego, se discute la determinaci'on del 'area para cada caso, las relaciones entre los radios de las circunferencias inscritas, circunscritas y excritas, las longitudes de las medianas, bisectrices y alturas. The principal theorems for solving oblicue triangles are presented. We shall show how to solve the five classical cases, and also some atipical cases, for instance, known the perimeter and two internal angles; or a lade, an angle between the other lades as like their sum. Finally, we shall discute how to calcule the area of triangles for the difference cases, the relations between the radii of inscribed, circunscribed and excribes circles, the lengths of medians, bisectors and heights.