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6.5 - Law of Sines
Section 6.5 Law of Sines
Chapter 6 – Trigonometric Functions: Right Triangle Approach
6.5 - Law of Sines
Law of SinesUsed for oblique triangles (triangles that do not
contain right angles).
6.5 - Law of Sines
Law of SinesWe have two possible cases for the law of sines.
Case 1 – One side and two angles (ASA or SAA)
Case 2 – Two sides and the opposite angle to one of those sides (SSA)
6.5 - Law of Sines
DefinitionLaw of Sines works when we have SAA or ASA.
6.5 - Law of Sines
Solving Using SAASolve the triangles below:a) b)
6.5 - Law of Sines
Solving Using ASASolve the triangles below:a) b)
6.5 - Law of Sines
The Ambiguous Case (SSA)
SSA is called an ambiguous case because the given information can result in zero, one, or two triangles.
6.5 - Law of Sines
SSA – No Triangle
6.5 - Law of Sines
SSA – One Triangle
6.5 - Law of Sines
SSA – Two Triangles
6.5 - Law of Sines
Examples - SSASolve ABC if A = 50, a = 10, and b = 20.
6.5 - Law of Sines
Examples - SSASolve ABC if A = 40, a = 54, and b = 62.
6.5 - Law of Sines
Example – pg. 474
6.5 - Law of Sines
Example – pg. 474
6.5 - Law of Sines
Example – pg. 474
6.5 - Law of Sines
Example – pg. 475
6.5 - Law of Sines
More PracticeSketch the triangle. Use the Law of Sines to solve
for all possible triangles that satisfy the given conditions. 22 , 95 , 420
a 28, 15, 110
a 30, 40, 37
a 20, 45, 125
b 45, 42, 38
A B a
b A
c A
c A
c C
16.
19.
20.
21.
22.