8.1.2 – Law of Sines Cont’d

SSA

• In the case of SSA, we have to be careful in regards to the third side– AAS or ASA is not as picky; having two angles gives

us the third• If we have an acute triangle, there a couple of

potential outcomes – 1) No triangle– 2) One, unique triangle– 3) Two triangles

• The so called “ambiguous” case has to do with the relation of the third side

• For our purposes, h = bsin(A)• As long as a = h OR h < a < b OR b ≤ a, a

triangle may exist• The obtuse case is much simpler; the third

side opposite the largest angle must be the largest side (corresponding sides/angles)

• Depending on the case, a triangle may or may not exist

• Example. Construct a triangle, is possible, for which:– A = 75 degrees– b = 15 units– a = 10 units

• If the triangle DOES exist, use the same methods as before to get our sides

• Example. Solve for the remaining angles, if possible, and side of any triangle that may be created given:– A = 40 degrees– a = 4– b = 4

• Example. Example. Solve for the remaining angles, if possible, and side of any triangle that may be created given:– A = 42 degrees– a = 3 units– b = 9 units

• Note: Names of sides and angles DO NOT matter. Just need a corresponding angle/side, and an additional one.

• Example. Solve for the remaining angles, if possible, and side of any triangle that may be created given:– C = 116 degrees– a = 24.1 units– c = 25 units

• Assignment• Pg. 612• 23-29 ODD (just tell me IF the triangle exists)• 31-41 ODD (do all parts)