This week in pre-calculus we learned about Sine Law and Cosine Law. These are used when trying to find side lengths or angles on triangles that are not right.

Sine Law

Sine Law is used when finding side lengths or angles on non-right triangles. There are two formulas, the original one used to find side lengths, and another one which is just reciprocated since it is easier to solve. Here they are:

Finding side length:

\frac {a}{sinA} = \frac {b}{sinB} = \frac {c}{sinC}

 

Finding angle:

\frac {sinA}{a} = \frac {sinB}{b} = \frac {sinC}{c}

 

The lowercase a, b, and c are all of the side-lengths on the triangle. The uppercase A, B, and C are then the angles.

To use Sine Law, you must plug in all of the values you know, and then use the two that have the most information in them to solve, as you should have only one variable. Here is an example:

 

\frac {a}{sin47} = \frac {b}{sinB} = \frac {12.5}{sin95}

 

You would then use \frac {a}{sin47} = \frac {12.5}{sin95}

 

Then you would simply solve for a.

Cosine Law

Cosine Law is used when you are unable to use Sine Law, (generally when there is no fraction with the top and bottom containing a number).

 

Finding side length:

a^2 = b^2 + c^2 - 2bc cosA

 

Finding angle:

cosA = \frac {c^2 + b^2 - a^2}{2bc}

 

To use Cosine Law you simply plug in all of the values you know and then solve for your unknown.