9-3

9-3 Law of Sines

Law of Sines is a method used to solve triangles that cannot be solved using SOHCAHTOA. Right now we are going to learn Law of Sines. Law of Sines is used with non right triangles. You can only use it if you have an angle and an opposite leg value you know. The formula to solve these triangles is: Sin(Angle)/Opposite Leg = Sin(Angle 2)/Opposite Leg 2 *Cross multiply to solve
Let’s try an example problem:

Example 1:
In triangle ABC angle B = 128°, side b = 14 and side c = 6. Determine whether or not angle C exists. If it does exist find all possible measures of angle C.

Sin 128°/14 = Sin C/6
6 Sin 14 = 14 Sin C
Sin C = 6 Sin 128°/14

At this point you will take the inverse = C = Sin-1(6 Sin 128°/14)
C = 72.435

Since you are taking the inverse you want two answers. So make your answer negative and add 180°.
-72.435 + 180 = 107.565

Your final answers are 72.435 & 107.565