# Section 6.5 Law of Cosines

```Class Work
1. Sketch a right triangle that has acute angle , and find the
five other trig ratios of .
7
cos  
25
2. Evaluate the expression without using a calculator.

  
 sin    cos 
4 
4

2
2
Class Work
3. Solve the triangle.
Section 6.5
Law of Cosines
Objectives:
•Use the Law of Cosines to solve
triangles.
•Use Heron’s Formula to find the area
of a triangle.
Law of Cosines:
If you need to solve for an angle you will want to
b2  c2  a 2
cos A 
2bc
a 2  c2  b2
cos B 
2ac
2
2
2
a b c
cos C 
2ab
Ex 1. Solve the triangle.
C
5
8
A
12
B
Ex 2. Solve the triangle.
C
76
39
A
63
B
Class Work
4. Use the Law of Cosines to solve for .
Ex 3. Solve ABC given A=25, b = 10, c = 20
EX 4. Solve for x.
Class Work
5. Solve for x.
6. Solve ABC given b = 60, c = 30, A=70.
7. Determine whether you need to use the Law of
Sines or the Law of Cosines to solve. Then find either
x or .
a)
d)
b)
c)
Heron’s Formula:
Ex 5. Find the area of the triangle with sides
a =15, b = 23, c = 16.
Class Work
8. Find the area of the triangle with sides a = 50, b = 17, c = 41.
HW #4
P513
2,3,5,8,9,12,19-22all,27,28
```