1. Law of Sines - Why do we need it? How is it derived from what we already know?
We use the law of sines when we don't have a right triangle. In previous concepts we were able to use the Pythagorean Theorem but were not able to use it in this concept because we are not dealing with right triangles. .Also like in the unit circle the restriction for sine is still applied (it can't be bigger than one). It is very important that you know that this law can only be used when we have ASA or AAS. The Law of Sines can be used when it comes to non-right triangles with AAS and ASA. This law was derived from a non-right angle triangle. To begin we drew a perpendicular line from the top of the triangle to the bottom and labeled that "h." Now that we have the two triangles the next step is to take the sin of A and C ( opposite/ hypotenuse). The next thing that we have to do is get h by itself so what we do is multiply both sides by its denominators as shown in the picture. In addition since both equations equal h we can set them equal to each other and we try to get sin by itself on top. So we obtain an answer of sinA/a= sinC/c.
Area of an Oblique Triangle:
1. How is the "area of an oblique" triangle derived?
The area of an oblique triangle is derived from the original area formula for triangles (A=1/2bh). Since the perpendicular line of the triangle is the height(h) and b is the base. While the oblique triangles area is one half of the product of two sides and the sine of their interior angle.
We know that sinC=h/a from previous concepts, so once you multiply 'a' on both sides h=a sin C, and plugging 'h' into that A=1/2bh formula we really have A=1/2b(a sin C).
How does it relate to the area formula you are familiar with?
It relates to the area formula were familiar with because there very similar the only difference is that h is replaced by the sin of the included angle. Another thing that we used that we had used in the past was SOHCAHTOA.
It relates to the area formula were familiar with because there very similar the only difference is that h is replaced by the sin of the included angle. Another thing that we used that we had used in the past was SOHCAHTOA.
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