Essential question: How do I solve oblique triangles? How do I use Law Of Sines – AAS, ASA, & 1st case of SSA to solve oblique triangles?

To “solve a triangle” is to find… CAPITAL LETTERS ARE ANGLES lower cased letters are sides To “solve a triangle” is to find… the lengths of all sides and… the measures of all angles. A C B a b c

...are triangles that have no right angles. Oblique Triangles ...are triangles that have no right angles. A C B a b c

To solve an oblique triangle you need to know To solve an oblique triangle you need to know... at least one side and two other parts of the triangle. 1) two angles and any side (ASA or AAS) 2) two sides and an angle opposite one of them (SSA) 3) three sides (SSS) learned yesterday 4) two sides and their included angle (SAS) learned yesterday

Law of Sines A C B a b c AAS ASA

Ex. Solve ABC, B=64°, C= 38° and b=9ft

Ex. 1 Solve ABC. C = 102.3°, B = 28.7°, and b = 27.4 feet C AAS A = 49º a a = 43.06 ft b B = 28.7º b = 27.4 ft B A c C = 102.3º c = 55.75 ft A = 180º - 102.3º - 28.7º = 49º

ASA Ex. 2 C = 180º - 43º - 98º Solve the triangle. A = 43° a = 23.84 ft C ASA B = 98º b = 34.62 ft b C = 39º c = 22 ft a 98° 43° 22 feet C = 180º - 43º - 98º = 39º

Ex. 7 The course for a boat race starts at point A and proceeds in the direction S52°W to point B, then in the direction S40°E to point C, and finally back to A. Approximate the total distance of the race course. 40° 52° 8 km A B C D The length of the race course will be a + b + c B = 180º – 40º – 52º The length of the race course will be 19.46 km = 88º 40° a = 6.31 c = 5.15

When did we have problems proving triangles congruent? When we had SSA. It is still a problem. When we have SSA, we can have no triangle that exist, we can have 1 triangle, or we can have 2 triangles. Let’s look….

SSA Ex. 4 Solve the triangle. A = 85° a = 15 ft B = b = 25 ft C = c = 25 feet No triangle exists.

What are your questions?