# Ratio of sides in a triangle vs ratio of angles?

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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It is true if the triangle is equilateral. –  Ross Millikan Jul 8 '12 at 0:23
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## 2 Answers

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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