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

    1.  Law of Sines

http://www.mathwarehouse.com/trigonometry/law-of-sines/images/formula-picture-law-of-sines2.png

Why do we need it?

• We need the law of sines because sometimes we are not dealing with right triangles. We don’t have the normal trig functions to solve non-right triangles. However, if we drop a perpendicular line h we can use the trig functions to help us solve the non-right triangles.

How is it derived?

• First, we cut the triangle in half. This reveals two right triangles within the non-right triangle. The law of sine’s are derived by taking the sine of angle A and angle C. we should end up with sinA= h/c & sinC= h/a Then we solve for h and simplify. This gives us c x sinA =h & a x sinC= h. If both equations are equal to h then they are both equal to each other. Now, to simplify this set a denominator of ac and cancel. You should end up with. SinA/a = SinC/c

2.   Area Formulas

• How is it related to the previously known formula? This formula is related to it because it is basically the same formula. The only difference is that we don’t know the value of h. to find the value of h we substitute (a x Sin C). In the next paragraph we will learn why and how we substitute this value.
• How is it derived?  The area formula is derived by finding the value of h. we know the are of a triangle is A= ½ bh. We know that SinC=h/a we solve for h, h= a x SinC. Plug this into the formula, A= ½ b( a x SinC ).