21 lines
1.2 KiB
Markdown
21 lines
1.2 KiB
Markdown
# Intro
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Tl;dr, the law of sines is:
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$$ \frac{\sin(\alpha)}{a} = \frac{\sin(\beta)}{b} = \frac{\sin(\gamma)}{c} $$
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Under convention:
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- Angle $\alpha$ is opposite side $a$
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- Angle $\beta$ is opposite side $b$
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- Angle $\gamma$ is opposite side $c$
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- Any triangle that is *not a right triangle* is called an oblique triangle. There are two types of oblique triangles:
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- **Acute triangles**: This is an oblique triangle where all three interior angles are less than $90\degree$ or $\dfrac{\pi}{2}$ radians.
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- **Obtuse Triangle**: This is an oblique triangle where one of the interior angles is greater than $90\degree$.
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## Different types of oblique triangles
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1. **ASA Triangle**: (Angle Side Angle) - We know the measurements of two angles and the side between them
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2. **AAS**: We know the measurements of two angles and a side that is not between the known angles.
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3. **SSA**: We know the measurements of two sides and an angle that is not between the known sides.
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These triangles can be solved by adding a line that goes from one vertex to intersect perpendicular to the opposite side, forming two right triangles ($h$).
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## Solving for the law of sines
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We know that $\sin\alpha = \dfrac{h}{b}$
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