Sections:

Law of Sines and Law of Cosines, Page 3

Law of Sines: Examples

Let’s take a look at some examples using the Law of Sines.

Example 1:

Given angle A equals 25 degrees, angle B equals 110 degrees and b = 40.1, solve triangle ABC (round your answer to the nearest tenth).

The first step is always to draw a diagram (this diagram is not drawn to scale): 

5.2.3 graphic 1

You can find the measure of angle C by remembering that the angles of any triangle add up to 180°. You can write the following equation:

the measure of angle C equals 180 minus the sum of 25 and 110, which equals 45 degrees

You can then find sides a and c by using the Law of Sines:

To find a:

a over sin(A) equals b over sin(B), so a over sin(25) equals 40.1 over sin(110)

Cross-multiply to get:

a*sin(110) = 40.1sin(25), so a = 40.1sin(25)/sin(110), so a = 18.0

To find c:

b/sin(B) = c/sin(C); 40.1/sin(110) = c/sin(45); 40.1sin(45) = c sin(110); c = 40.1sin(45)/sin110); so c = 30.2