Section 6.2 Law of Cosines!

Proof of the Law of Cosines

The law of cosines can be written in 6 ways depending on which angle or side is being solved for.

Applications of the Law of Cosines
1. SSS (solving for the angles)

***TIP: Solve for the angle opposite the largest side first***
If the cosine of the angle is greater than 0, the angle is acute
If the cosine of the angle is less than 0, the angle is obtuse

Now that the ratio of the sine of angle B to side b is available, it is easiest to use the law of sines to find the next angle.
Also, since angle B is obtuse, both angles A and C must be acute.

The last angle, angle C, can be calculated easily knowing that all the angles in a triangle add up to pi.

1. SAS (solving for the remaining side)

Heron's Area Formula
~Can be used to calculate the area of any triangle where the lengths of all 3 sides are known

Where s is the semi perimeter, or:

The area of the triangle is 11.40 square meters

The Law of Cosines is...
As easy as 3.141592(pi!)