TT-3+Law+of+Sines

Chapter 6: Law of Sines (pgs. 408-416)
When solving a triangle, you must find all the missing sides and angles. When there is a right triangle, you can use right triangle trig (SOHCAHTOA). Remember to always try and work with information you already have (avoid using calculated numbers). The Law of Sines is used to solve for oblique triangles. For this to work, there must be at least one pair (angle measure and its corresponding side). One of the first things that you need to remember about oblique triangles is that there can be none, one, or two triangles.

1) Two angles and any side (AAS or ASA) 2) Two sides and an angle opposite one of them (SSA) 3) Three side (SSS) 4) Two sides and their included angle.

So how do you know how many triangles there are? 1) If 0 < a < h, there will be no triangle (no solution) 2) a=h, right triangle= one solution 3) If h < a < b, two triangles



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 * __Vocabulary for 6.1 Law of Sines__//**

**Law of Sines:** It states that each side of a triangle is proportional to the sine of the opposite angle. For example: The law of sines can be used when two angles and a side of a triangle are known.

**Ambiguous:** When the case is ambiguous, it means the triangle could be open to two or more interpretations. In other words, an ambiguous case is when two sides and an angle opposite one of them are known. Based on whether the angle is acute or obtuse, the solutions may vary.


 * Oblique triangle:** Triangles that have no right angles. When solving an oblique triangle, you must first know the measure of at least one side and the measure of any two sides, two angles, or one angle and one side.

**AAS or ASA:** two angles and any side

**SSA:** two sides and an angle opposite one of them

**SSS:** three sides

**SAS:** two sides and their included angle

**HL:** hypotenuse leg