BQ# 1 Unit P Concept 1 & 4 Law of Sines Derivation and Area of an Oblique Triangle

1. Law of Sines - Law of Sines is important because life isn't so perfect that it will always give right triangles. Normal trig functions that we use for special right triangles don't apply to non-right triangles. Therefore we use the law of Sines to solve non-right triangles. Essentially, what we do is set a perpendicular from angle B to create two right triangles and label the line as H. From here we can determine the relationships and use the transitive property
c Sin A = a Sin C to solve for what is needed. From this, we can solve for any side or angle depending on it opposite angle or side. This video below will help you fully understand the concept of Law of Sines.

 

4. Area Formulas - Sometimes you might not be able to get the value of H from the law of Sines. Not to fear because the area of an oblique triangle is very similar to the area of a triangle (A=1/2bh) but since we don't know H, we use (A=1/2b(asinc). This will help us find the value of H so we can use either law of sines or cosines to determine the rest of the triangle if needed. Remember, "The area of an oblique (all sides different lengths!) triangle is one half of the product of two sides and the sine of their included angle." This video below will help you understand this situation better.




Sources
Law of Sines Deriviation
Area of an Oblique Triangle Deriviation