diff --git a/education/math/MATH1060 (trig)/Law of Sines.md b/education/math/MATH1060 (trig)/Law of Sines.md index 107b1a1..bf62b11 100644 --- a/education/math/MATH1060 (trig)/Law of Sines.md +++ b/education/math/MATH1060 (trig)/Law of Sines.md @@ -1,7 +1,20 @@ # Intro Tl;dr, the law of sines is: $$ \frac{\sin(\alpha)}{a} = \frac{\sin(\beta)}{b} = \frac{\sin(\gamma)}{c} $$ +Under convention: +- Angle $\alpha$ is opposite side $a$ +- Angle $\beta$ is opposite side $b$ +- Angle $\gamma$ is opposite side $c$ - Any triangle that is *not a right triangle* is called an oblique triangle. There are two types of oblique triangles: - **Acute triangles**: This is an oblique triangle where all three interior angles are less than $90\degree$ or $\dfrac{\pi}{2}$ radians. - - **Obtuse Triangle**: This is an oblique triangle where one of the interior angles is greater than $90\degree$. \ No newline at end of file + - **Obtuse Triangle**: This is an oblique triangle where one of the interior angles is greater than $90\degree$. +## Different types of oblique triangles +1. **ASA Triangle**: (Angle Side Angle) - We know the measurements of two angles and the side between them +2. **AAS**: We know the measurements of two angles and a side that is not between the known angles. +3. **SSA**: We know the measurements of two sides and an angle that is not between the known sides. +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 ($h$). + +## Solving for the law of sines +We know that $\sin\alpha = \dfrac{h}{b}$ +