1. Area = ½ bc sinA = ½ ab sinC = ½ ac sinB
The area of an oblique triangle can be found by using the following 
formula:
Area = ½ bc sinA  =  ½ ab sinC  =  ½ ac sinB
Since not all triangles are labeled A,B,C, you should remember 
that the AREA of a triangle =
1/2 the product of _________and the sine of ___________.

2. Area = ½ bc sinA = ½ ab sinC = ½ ac sinB
Find the area of each triangle described below.
1) A = 36o, b = 3 feet, c = 5 feet
Area = ½ bc sinA = ½ ab sinC = ½ ac sinB

3. Area = ½ bc sinA = ½ ab sinC = ½ ac sinB
2) C = 100o, a = 12 inches, b = 10 inches
Area = ½ bc sinA = ½ ab sinC = ½ ac sinB

4. Continuing our discussion of dealing with oblique (non­right)
 triangles, today we will look at the Law of Cosines.  
Yesterday we talked finished talking about Law of Sines. (Used 
with:
AAS
ASA
SSA *check for ambiguous cases! - 0,1, or 2 Triangles
Law of Cosines is used for:
SAS
SSS
when there isn't an angle and opposite side pair

5. a2 =b2+c2 -2bc cosA b2 =a2+c2 -2ac cosB c2 =a2+b2 -2ab cosC
Law of Cosines
a2 =b2+c2 -2bc cosA
b2 =a2+c2 -2ac cosB
c2 =a2+b2 -2ab cosC

6. a2 =b2+c2 -2bc cosA b2 =a2+c2 -2ac cosB c2 =a2+b2 -2ab cosC
Use the law of cosines to find the missing sides and angles. C
a2 =b2+c2 -2bc cosA
b2 =a2+c2 -2ac cosB
c2 =a2+b2 -2ab cosC 8 a
700 B 6 A

7. a2 =b2+c2 -2bc cosA b2 =a2+c2 -2ac cosB c2 =a2+b2 -2ab cosC
Use the law of cosines to find the missing sides and angles. C
a2 =b2+c2 -2bc cosA
b2 =a2+c2 -2ac cosB
c2 =a2+b2 -2ab cosC 7 8 A 12 B

8. Area = 1/4 √ p(p-2a)(p-2b)(p-2c)
Another method for finding the area of a triangle 
(if we do not know the height) is Heron's Formula,
 which is based on the perimeter, p, of the triangle,
 p = a + b + c.
Area = 1/4 √ p(p-2a)(p-2b)(p-2c)

9. use law of cosines to find an a
Recap!
Draw and label triangle.
Decide which law to use base on similarity theorem.
AAS ASA SSA
SAS SSS
check ambiguous
cases for how
many triangles
use law of cosines to find an a
missing piece
use law of sines to find
missing measures
use law of sines to find
missing measures
Find Area