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
Ratio of sides in a triangle vs ratio of angles?
3
$\begingroup$
euclidean-geometry
-
0It is true if the triangle is equilateral. – 2012-07-08
2 Answers
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:
The sides are in the ratio $1:1:\sqrt{2}$, while the angles are in the ratio $1:1:2$.