diff --git a/education/math/MATH1060 (trig)/Law of Sines.md b/education/math/MATH1060 (trig)/Law of Sines.md index bf62b11..6a1c6ef 100644 --- a/education/math/MATH1060 (trig)/Law of Sines.md +++ b/education/math/MATH1060 (trig)/Law of Sines.md @@ -16,5 +16,18 @@ Under convention: 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 $\sin\alpha = \dfrac{h}{b}$ +We know that $\sin\alpha = \dfrac{h}{b}$ and $\sin\beta = \dfrac{h}{a}$. We can sole both equations for $h$ to get: +- $h = b\sin\alpha$ +- $h = a\sin\beta$ +Setting both equations equal to each other gives us: +$b\sin\alpha = a\sin\beta$ +Multiply both sides by $\dfrac{1}{ab}$ gives yields $\dfrac{\sin\alpha}{a} = \dfrac{\sin\beta}{b}$ + +# SSA triangles +Side side angle triangles may be solved to have one possible solution, two possible solutions, or no possible solutions. + +- No triangle: $a < h$ +- One triangle: $a \ge b$ +- Two triangles: $h < a < b$ +- One right triangle: $a = h$