Class Work1. Sketch a right triangle that has acute angle , and find the

five other trig ratios of .

2. Evaluate the expression without using a calculator.

7cos

25in quad IV

2 2

sin cos4 4

Class Work

3. Solve the triangle.

Section 6.5Law 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 use these formulas instead.

2 2 2

2 2 2

2 2 2

cos2

cos2

cos2

b c aA

bc

a c bB

ac

a b cC

ab

Ex 1. Solve the triangle.

BA

C58

12

Ex 2. Solve the triangle.

A B

C

39

63

76

Class Work4. 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 Work5. 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) b) c)

d)

Heron’s Formula:

Ex 5. Find the area of the triangle with sides a =15, b = 23, c = 16.

Class Work8. 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