BQ#1: Unit P Concept 1-5- Law of Sines AAS or ASA, Area of an oblique triangle.

1. Law Of Sines-

     The law of sines is needed when you are not working with a non-right triangles. This helps us with  the trig functions that are used for solving non-right triangles.
How is derived:
1.)

To create a right triangle we must drop a perpendicular line from angle B and it can be labeled as h.  Two right triangles are now created. To use the law of sines, two sides and two angles must be present.

2)

To find the missing parts of a triangle the following relationships are needed.  To find h you can use the transitive property and have cSineA=aSineC, since they both equal h.

3)

If you divide both side by ac then SinA/a= SinC/ c. This is one of the relationships used in the law of sines. The ratios can be used to find any parts of a non-right triangle.

4. Areas formulas: 

The area of an oblique triangle cannot be found without the value of h. The area of a right triangle is A= 1/2bh, where b is the base and h is the height of the triangle.

In this triangle sinC=h/a and we know that h=asinc. We substitute h for asinc in the are formula which is A=1/2bh. The new formula is A=1/2b(asinc) The area of an oblique triangle is one half of the product of two sides and the sine of the given angle. The angle that we are trying to find must be in between the two sides that were given. Two sides and a angle must always be present. The angle will always be sine of the given angle.