Law of Sines

Law of Sines is used on non-right triangles. When you take the inverse, you will get two answers. You use Law of Sines when you now an angle and its opposite leg. You will have to cross multiply and divide in this section.

Formula: SinA/a = SinB/b = SinC/c

Example 1: Find the missing angle and the lengths of c and b.

A

C B
First, we have to find the missing angle. Since you already have two of the angles, all you have to do is subtract the two angles you already have form 180 to get the third angle.

180-40-80 = 60 degrees

Now, let's solve for c and b. This is when Law of Sines comes in.

Sin80/14 = Sin60/b

bSin80 = 14Sin60

b = 14Sin60/sin80

b = 12.311

Sin80/14 = Sin40/c

cSin80 = 14Sin40

c = 14Sin40/Sin80

c = 9.138

Example 2: Find angle A and the lengths of b and c.

A

C B

180-41-88 = 51 degrees

Sin41/20 = Sin88/b

bSin41 = 20Sin88

b = 20Sin88/Sin41

b = 30.466

Sin41/20 = Sin51/c

cSin41 = 20Sin51

c = 20Sin51/sin41

c = 23.691