http://www.ck12.org Chapter 4. Basic Triangle Trigonometry
Solution:
sin 17◦= 14 h
h=14 sin 17◦≈ 4. 0932 ...Sincea=h, this information forms exactly one triangle and angleCmust be 90◦.
Example C
(^6) A= 22 ◦,c=11 anda=9. If possible, find (^6) C.
Solution:
sin 22◦= 11 h
h=11 sin 22◦≈ 4. 12 ...
Sinceh<a<c, there must be two possible angles for angleC.
Apply the Law of Sines:
9
sin 22◦=11
sinC 1
9 sinC 1 =11 sin 22◦
sinC 1 =11 sin 22◦
9
C 1 =sin−^1(11 sin 22◦
9)
≈ 27. 24 ...◦
C 2 = 180 −C 1 = 152. 75 ...◦
Concept Problem Revisited
SSA is not a method from Geometry that shows two triangles are congruent because it does not always define a
unique triangle.
Vocabulary
Ambiguousmeans that the given information may not uniquely identify one triangle.