side opposite given angle - st. johns county school district · pclesson 6.1(b)_notes.notebook...
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PCLesson 6.1(b)_notes.notebook December 02, 2015
6.1(b) Law of Sines
Students will be able to . . .
• use the Law of Sines to solve oblique triangles (AAS, ASA, or SSA).
• find areas of oblique triangles and use the Law of Sines to model and solve reallife problems.
If two sides and one opposite angle are given, then three possible situations can occur: (1) no such triangle exists, (2) one such triangle exists, or (3) two distinct triangles satisfy the conditions.
Given angle
nonopposite side
h
side opposite given angle
PCLesson 6.1(b)_notes.notebook December 02, 2015
h
A
b
Given : Angle (A), side (a), side (b)
Determine how many triangles can be made with each of the lengths of a.
a1a2 a4 a5
a3
PCLesson 6.1(b)_notes.notebook December 02, 2015
a < h no triangle formed
a = h 1 triangle formed (right triangle)
a = b 1 triangle formed (isosceles)
A
bh
a
B
h < a < b 2 triangles formed
A
b
B2A
b
B1
A
b
B2A
b
B1
A
bh
a
A
b ha
B
a > b one triangle formed
A
bh
a
h = b sin A
PCLesson 6.1(b)_notes.notebook December 02, 2015
Examples
Use the Law of Sines to solve the triangle. If two solutions exist, find both.
(a) A = 58o, a = 4.5, b = 12.8
(b) A = 78o, a = 207, c = 210