Law of Cosines
REMEMBER
•We only use
SOH CAH TOA
when we are
solving
• So what do we use to solve triangles
that are NOT right triangles?
– Law of Cosines
• Use this when you are given:
– SAS ( side, included angle, side)
or
– SSS (all three sides)
• a2 = b2 + c2 – 2bc Cos A
– If solving for
A then Cos A = b2 + c2 - a2
2bc
• b2 = a2 + c2 – 2ac Cos B
– If solving for
B then Cos B = a2 + c2 - b2
2ac
• c2 = a2 + b2 – 2ab Cos C
– If solving for
C then Cos C = a2 + b2 - c2
2ab
• WHEN SOLVING FOR ANGLES USE
COS-1
• USE THE OTHER FORMULAS WHEN
SOLVING FOR SIDES (lowercase
letters)
The book tends to solve the triangles in
alphabetical order, so if you don’t, then your answer
might be a little off form the book or other
classmates.
Example 1
• What are we looking for?
First
– Side a
• What formula do we use if we are looking for
side a?
– a2 = b2 + c2 – 2bc Cos A
• Plug in a solve:
a2 = 62 + 132 – 2(6)(13) Cos 36
a2 =(put all this in your calculator)
a2 = 78.793 take the square root
remember to use exact hit 2nd ANS (-)
a = 8.9
Second
• What are we looking for?
– angle B
• What formula do we use if we are looking for angle
B?
– Cos B = a2 + c2 - b2
2ac
• Plug in and solve:
Cos B = (8.92 + 132 – 62)
(2*8.9*13)
Looking for angle so use inverse (2nd Cos 2nd Ans)
Cos-1(212.21/231.4)
23.5° = angle B
Third
• What are we looking for?
– angle C
• What formula do we use if we are looking for
angle C?
– We already know two of the angles
180° – (36° + 23.5°) or 180° - 36° - 23.5°
120.5° = angle C
Remember
• We went in alphabetical order
– a, B, C
• Don’t say you didn’t understand
• Use the examples we just worked and
in your book
Classwork/Homework
Go in alphabetical order
Application problems