Triangle Warm-up

Can the following side lengths be the side lengths of a triangle?

Law of Sinesand

Law of Cosines

• Solving Triangles Flow Chart

Law of Sines

If you know the measures of two angles and one side of a triangle, you can find the other two sides of the triangle by using the Law of Sines

In other words, if you are given ASA or AAS, use the Law of Sines.

Let’s Discover the Law of Sines

1) Find h in terms of a and the sine of an angle

2) Find h in terms of b and the sine of an angle

3) Use algebra to show

b

B

a

A sinsin

B

C

A c

ba

h

Use Triangle ABC

Let’s Discover the Law of Sines

4) Find k in terms of c and the sine of an angle

5) Find k in terms of b and the sine of an angle

6) Use algebra to show

b

B

c

C sinsin

Use Triangle ABC

k

B

C

A c

ba

Law of Sines

For a triangle with angles A, B, and C and sides of lengths a, b, and c (a opposite A, b opposite B, and c opposite C),

c

C

b

B

a

A sinsinsin

Example 1

Solve the triangle.

3859B

C

A

b350 cm

Example 2

Solve the triangle and find the area.

69

B

C

A

150 cm250 cm

Example 3

Solve the triangle and find the area.

38

21

24

P

A

L

Law of Cosines

Law of Cosines

For any triangle with sides of lengths a, b, and c, and with C the angle opposite the

side with length c,

Cabbac cos2222

Example 4

Solve the triangle and find the area.

36

52 cm

r

45 cm

C R

T

Example 5

Solve the triangle and find the area.

225 cm

175 cm

250 cm

Q E

D