8.7. Extension: Laws of Sines and Cosines http://www.ck12.org
11.m^6 A= 64 ◦,AB= 29 ,AC= 34
12.m^6 C= 133 ◦,m^6 B= 25 ◦,AB= 48Use the Law of Sines to solve 4 ABCbelow.
13.m^6 A= 20 ◦,AB= 12 ,BC= 5Recall that when we learned how to prove that triangles were congruent we determined that SSA (two sides and an
angle not included) did not determine a unique triangle. When we are using the Law of Sines to solve a triangle and
we are given two sides and the angle not included, we may have two possible triangles. Problem 14 illustrates this.
- Let’s say we have 4 ABCas we did in problem 13. In problem 13 you were given two sides and the not
included angle. This time, you have two angles and the side between them (ASA). Solve the triangle given
thatm^6 A= 20 ◦,m^6 C= 125 ◦,AC= 8. 4 - Does the triangle that you found in problem 14 meet the requirements of the given information in problem
13? How are the two differentm^6 Crelated? Draw the two possible triangles overlapping to visualize this
relationship.
It is beyond the scope of this text to determine when there will be two possible triangles, but the concept of the
possibility is something worth noting at this time.