7.1, 7.2, 7.3 Law of Sines and Law of Cosines

Cases: SSS – Given three sides. SAS – Given two sides and the included angle. SSA – Given two sides and the angle opposite one of them. ASA and AAS – Given two angles and one side.

Hints: Use Law of Sines when given: AAS or ASA : 2 angles and the side opposite; 2 angles and an included side – 1 solution SSA : two sides and an angle opposite one of them -- 1, 2, or no solutions

Hints: Use Law of Cosines when given: SAS : 1 solution SSS : 1 or no solution - For no solution: The sum of the two smallest sides must exceed the third side.

The Law of Sines In any triangle ABC, You only use two pieces to solve for the missing side or angle.

The Law of Sines Example:

The Law of Sines Ex. 2

The Law of Sines Ex. 2 Continued:

The Law of Sines Questions on Law of Sines? Don’t forget to check cases first, so that you know how many solutions you should have for each problem.

The Law of Cosines In any triangle ABC,

The Law of Cosines The Law of Cosines can solve for an angle or for a side. The following are the Law of Cosines solved for the angle. You only have to memorize the first set of formulas. You can use algebra to solve for the angle.

The Law of Cosines One important rule: In solving a triangle (finding all the sides and all the angles) , if you start with Law of Cosines and want to switch to Law of Sines – You must solve for the smallest angle first! If angle C is a right angle, Cos C = 0 and the Law of Cosines reduces to Pythagorean Theorem

The Law of Cosines Example:

The Law of Cosines Example:

The Law of Cosines Questions? Don’t forget with SSS to check for a solution first, before you attempt to solve the problem. Domain of sine and cosine… Practice worksheet