Download Algebra II/Trigonometry Honors Unit 9 Day 6: Law of Cosines

Algebra II/Trigonometry Honors
Unit 9 Day 6: Law of Cosines
Objective: To use the Law of Cosines to solve for missing sides and angles in non-right triangles
Key Concepts:
To solve for missing sides or angles in right triangles, you used _______________________
To solve for missing sides or angles in non-right triangles, we will use ___________________
The Law of Cosines can be used when you have:

SAS (you know two sides, and you know the angle between the two sides)

SSS (you know all three sides)
If ABC has sides of length a, b, and c as shown, then:
a 2  b 2  c 2  2bc  cos A
b 2  a 2  c 2  2ac  cos B
c 2  a 2  b 2  2ab  cos C
The formulas above can be solved for the cosine of an angle as well. You will need to use the
inverse cosine to solve each of the following:
b2  c2  a2
cos A 
2bc
a2  c2  b2
cos B 
2ac
a2  b2  c2
cos C 
2ab
Notes about triangle:

 A is across from side a,  B is across from side b, and C is across from side c.

Lowercase letters are sides. Uppercase letters are angles.
Example 1: Solve a triangle for the SAS case
Solve ABC with a  11 , c  14 , and B  34 (Draw a picture)
Example 2: Solve a triangle for the SSS case
Solve ABC with a  12 , b  27 , and c  20 .
Example 3: Use the law of cosines in real life
Scientists can use a set of footprints to calculate an organism’s step angle, which is a measure of
walking efficiency. The closer the step angle is to 180 , the more efficiently the organism
walked. The diagram at the right shows a set of footprints for a dinosaur. Find the step angle B.
HW: Page 596, #8-20 evens, plus worksheet