3
$\begingroup$

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

  • 0
    It is true if the triangle is equilateral.2012-07-08

2 Answers 2

9

This is false. The sides and angles are related by the law of sines: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

4

No, it is not true. Consider a 45-45-90 right triangle:

enter image description here

(image from Wikipedia)

The sides are in the ratio $1:1:\sqrt{2}$, while the angles are in the ratio $1:1:2$.