Given a triangle with the ratio of sides being $X: Y : Z$, is it true that the ratio of angles is also $X: Y: Z$? Could I see a proof of this? Thanks
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This is false. The sides and angles are related by the law of sines: $$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$ |
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No, it is not true. Consider a 45-45-90 right triangle:
The sides are in the ratio $1:1:\sqrt{2}$, while the angles are in the ratio $1:1:2$. |
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