Capítulo 15 · Neste capítulo você vai

Any triangles

  • demonstrate and apply the law of sines;
  • use the metric relations in any triangle and the law of cosines;
  • recognize whether a triangle is acutangle, rectangle or obtuse from the sides;
  • calculate medians, heights and angle bisectors depending on the sides;
  • use the Stewart relation.

Pythagoras’ theorem only applies to right triangles. In this chapter, he gains two generalizations that apply to any triangle — the law of sines and the law of cosines — and a tool to calculate any segment that connects a vertex to the opposite side: the Stewart relation. These are the formulas that surveyors, navigators and engineers use when the triangle does not have a right angle.

Abu al-Wafa (940–998), Persian astronomer who organized trigonometric functions and their tables.
Abu al-Wafa (940–998), Persian astronomer who organized trigonometric functions and their tables.
Regiomontanus (1436–1476), who brought triangle trigonometry to Europe.
Regiomontanus (1436–1476), who brought triangle trigonometry to Europe.
Matthew Stewart (1717–1785), Scottish mathematician.
Matthew Stewart (1717–1785), Scottish mathematician.
Some General Theorems (1746), book in which Stewart published the relationship that bears his name.
Some General Theorems (1746), book in which Stewart published the relationship that bears his name.