**1. Law of Sines**

**Why do we need it?**We need the Law of Sines in order to solve for a triangle that are not right triangle. While for a right triangle we can just use the Pythagorean Theorem to find missing angles and sides.

**How is it derived and what we already know?***First lets look at a triangle, we know that it is not a right triangle because it does have a 90 degree angle label.*

*http://math.ucsd.edu/~wgarner/math4c/derivations/trigidentities/lawofsines.htm*

*To make a triangle a right triangle, we must draw a line from the angle C to line AB. The red line we call it perpendicular line and label it*

*h*, now we have 2 right triangles. We know that it is a right triangle because it has a square box, which means it is 90 degree angle.

Lets recall the area of the right triangle to be Area = 1/2 base times height. To find the area of the triangle, we know that sin A = h/c and that sin c = h/a. Then we divide them the first one by c and the second by a. To get csinA = h and asinC = h.

*http://math.ucsd.edu/~wgarner/math4c/derivations/trigidentities/lawofsines.htm*

**To find angle B, we must make a perpendicular line from angle A to BC. Then use sinB = h/c and angle C is sinC = h/b.**

**That will give us the formula for Law for Sines, which is:**

http://www.mathsisfun.com/algebra/trig-sine-law.ht

*http://math.ucsd.edu/~wgarner/math4c/derivations/trigidentities/lawofsines.htm*

__4. Area of an Oblique Triangle__*An oblique triangle is a triangle with all sides with different length.*

**How is the area of an oblique triangle derived?**Since we know that sinC = h/a, sinB = h/a, and sinA = h/c. We multiply them by their denominator and you will get:

*http://wps.prenhall.com/wps/media/objects/551/564474/StudyGuide/7c1h7_1.gif*

http://www.compuhigh.com/demo/lesson07_files/oblique.gif

**How does it relate to the area formula that you are familiar with?**It basically uses the same formula, you just plug into the equation and find the area. We just need to use sine in order to find the height.

**References:**

http://www.mathsisfun.com/algebra/trig-sine-law.html

http://math.ucsd.edu/~wgarner/math4c/derivations/trigidentities/lawofsines.htm

http://wps.prenhall.com/wps/media/objects/551/564474/StudyGuide/7c1h7_1.gif

http://www.compuhigh.com/demo/lesson07_files/oblique.gif

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