Law of Sines

Triangles Review

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

Discussion

• How have we solved for missing sides and angles in triangles thus far? What types of triangles have we solved?

“Solving” a triangle means finding the missing sides and angles.

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

Find the length of side AC in triangle ABC

3859B

C

A

b350 cm