Download CLASS 1 CHARACTERISTICS of FUNCTIONS, ALGEBRAICALLY

Chapter 6 – Trigonometric Functions:
Right Triangle Approach
6.5 - Law of Sines
Law of Sines

Used for oblique triangles (triangles that do not
contain right angles).
6.5 - Law of Sines
Law of Sines

We 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
Definition

Law of Sines works when we have SAA or ASA.
6.5 - Law of Sines
Solving Using SAA
Solve the triangles below:
a)
6.5 - Law of Sines
b)
Solving Using ASA
Solve the triangles below:
a)
6.5 - Law of Sines
b)
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 - SSA

Solve ABC if A = 50, a = 10, and b = 20.
6.5 - Law of Sines
Examples - SSA

Solve 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 Practice

Sketch the triangle. Use the Law of Sines to solve for
all possible triangles that satisfy the given conditions.
16.
A  22,
B  95,
a  420
19. a  28,
b  15,
A  110
20. a  30,
c  40,
A  37
21. a  20,
c  45,
A  125
22. b  45,
c  42,
C  38
6.5 - Law of Sines