Section 5-5 Law of Sines

Section 5-5 solving non-right triangles Law of Sines solving triangles AAS or ASA solving triangles SSA Applications

Solving Non-Right Triangles In Chapter 4 we learned to solve right triangles, which meant that we could find all its missing parts In the next two sections, we will learn to solve non-right triangles using two new tools: the Law of Sines and the Law of Cosines Which tool we use depends upon which parts we are given

Solving Non-Right Triangles Law of Sines  ASA – two angles and the included side  AAS – two angles and a non-included side  SSA – two sides and a non-included angle Law of Cosines  SSS – three sides  SAS – two sides and the included angle

Law of Sines For any ΔABC with angles A, B, and C and opposite sides a, b, and c, respectively: Either version can be used, but it is easier if the missing variable is in the numerator

AAS and ASA since both AAS and ASA form a triangle congruence (from geometry), there is exactly one triangle that can be formed using the three parts when solving either of these types of triangles, you are looking for only one possible solution

SSA – The Ambiguous Case you might recall from geometry that SSA is not a congruence postulate or theorem If given SSA, there are three possible results  No triangle is formed  One triangle is formed  Two triangles are formed

A forest ranger at ranger station A sights a fire in the direction 32  east of north. A ranger at station B, 10 miles due east of A, sights the same fire on a line 48  west of north. Find the distance from each ranger station to the fire.