9-3 Law of Sines!

This week I am going to explain how to solve triangles using the law of sines.

This is only used when you know an angle and an opposite leg. This is also only used on non-right triangles.

The formula for these types of problems is:

sin A/a=sin B/b=sin C/c

Note: To solve this formula, you are going to cross multiply.

Now I am going to work a few examples of these types of problems.

Example 1:

You are going to solve for b and c. To do this you will use the formula given above. Lets solve for b first.

We are going to use Angle A to help solve for both side lengths because that side length is already given.

1. Sin 45 degrees/14=Sin 60 degrees/b
2. bSin 45 degrees=14Sin 60 degrees
3. b=14Sin 60 degrees/Sin 45 degrees
4. b=17.149

Now we are going to solve for c.

1. Sin 45 degrees/14=Sin 75 degrees/c
2. cSin 45 degrees=14 Sin 75 degrees
3. c=14Sin 75 degrees/Sin 45 degrees
4. c=19.129

Example 2:

You are going to solve for a and c. We are going to use Angle B because the side length is already given for that one. We are going to solve for a first.

1. Sin 30 degrees/9=Sin 105 degrees/a
2. a=Sin 30 degrees=9Sin 105 degrees
3. a=9Sin 105 degrees/Sin 30 degrees
4. a=17.388

Now lets solve for c.

1. Sin 30 degrees/9=Sin 45 degrees/c
2. cSin 30 degrees=9Sin 45 degrees
3. c=9Sin 45 degrees/Sin 30 degrees
4. c=12.726

And that is how you use Law of Sines to solve for triangles!

--Halie! :)