## Archive for November, 2011

2011-11-07

The octahedron is a Platonic solid, which means it is made of all regular polygons for each face, being eight equilateral triangles arranged four at each vertex. With edge length of S, the surface area would be that of 8 equilateral triangles, $$8\cdot S^2\cdot \frac{\sqrt3}{4}=2\cdot …Read the Rest ### Law of Sines and Cosines 2011-11-07 The law of cosines relates the sides and angles of a triangle. \(a^2=b^2+c^2-2bc\cdot \cos\alpha \\ b^2=a^2+c^2-2ac\cdot \cos\beta \\ c^2=a^2+b^2-2ab\cdot \cos\gamma$$ It can also be rearranged to: $$\large\alpha=\arccos\left(\frac{b^2+c^2-a^2}{2bc}\right) \\ \large\beta=\arccos\left(\frac{a^2+c^2-b^2}{2ac}\right) \\ \large\gamma=\arccos\left(\frac{a^2+b^2-c^2}{2ab}\right)$$ As long as all three sides or at least one side and two angles …Read the Rest

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