4A.1 - Law of Sines

each side of a triangle is proportional to the sine of the opposite angle

law of sines

• ex. sin A/a = sin B/b

uppercase

angles are

lowercase

sides are

aas

angle angle side

asa

angle side angle

ssa

side side angle

the ambiguous case

ssa ONLY!

• if two sides and one opposite angle are given, three situations are possible

  • no complete triangle

  • one triangle

  • two triangles

step 1

draw and label triangle

step 2

determine aas, asa, or ssa

step 3

make answer table

step four

complete all sides/angles

checking case (ONLY SSA)

• if not already achieving error, subtract first found angle from 180 degrees

• add angle given in problem

• if answer > 180, one triangle is possible

• if answer < 180, two triangles are possible

if two triangles

• keep all given

• use first step solution as first angle found of second triangle

• subtract known angles from 180 for last angle

• solve for sides