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 ODD (just tell me IF the triangle exists) ODD (do all parts)