BQ#1: Unit P: Concept: 1 & 4: Law of Sines and Area Formulas

1. Law of Sines - Why do we need it?  How is it derived from what we already know?

The Law of Sines is used when we are trying to derive triangle that is not a right triangle.

We start with a non-right triangle. we drop an imaginary perpendicular line from <B and make two right triangles.

We call the height of the triangles h. Since they are now two right triangles, we can use the basic sig function. SOHCAHTOA. SinA= h/c. SinC=h/c. We use basic algebra to manipulate them.

Since both SinA/a=h and SinC/c=h, this means that SinA/a=SinC/c

4. Area formulas - How is the “area of an oblique” triangle derived?  How does it relate to the area formula that you are familiar with?

The area of an oblique triangle os 1/2 of the product of 2 sides and the sin of their included angle.

Well we all know that the formula for a triangle is A=1/2bh where b is the base and h is the height.

the height is unknown so we use sinC=h/a.

We need to get "h" by itself so we just multiply the a to the other side so h=aSinc. We now know h so we plug it into the area formula (A=1/2baSinC)