4.6. Law of Sines http://www.ck12.orgCase 1:a<h
Simply put, sideais not long enough to reach the opposite side and the triangle is impossible.
Case 2:a=h
Sideajust barely reaches the opposite side forming a 90◦angle.
Case 3:h<a<c
In this case sideacan swing toward the interior of the triangle or the exterior of the triangle- there are two possible
triangles. This is called the ambiguous case because the given information does not uniquely identify one triangle.
To solve for both triangles, use the Law of Sines to solve for angleC 1 first and then use the supplement to determine
C 2.
Case 4:c≤a
In this case, sideacan only swing towards the exterior of the triangle, only producingC 1.
Example A(^6) A= 40 ◦,c=13, anda=2. If possible, find (^6) C.
Solution:
sin 40◦= 13 h
h=13 sin 40◦≈ 8. 356
Becausea<h( 2 < 8. 356 ), this information does not form a proper triangle.
Example B
(^6) A= 17 ◦,c=14, anda= 4. 0932 ...If possible, find (^6) C.