# Tag Info

## Hot answers tagged triangles

Accepted

### Interesting property about triangles I don't know about.

The answer is on the comments. According to Calvin Lin it's a "well known" olympiad problem. A more elegant proof that mine involves 60 degrees rotations. IE, BCC' and BA'A are the same ...
• 171
Accepted

### How to show that given two acute angles, the sine ratio of the greater angle is greater than the sine ratio of lesser angle?

Let us consider $\triangle{ABC}$ such that $\angle{ABC}=\psi$ and $\angle{ACB}=\theta$. Let $D$ be a point on $BC$ such that $AD\perp BC$. We use the following claim. A proof of the claim is written ...
• 135k
1 vote

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1 vote

### How to show that given two acute angles, the sine ratio of the greater angle is greater than the sine ratio of lesser angle?

Consider a circle of radius $1$ centered at the point $O$. Fix any point $A$ on the circle. Fix a point $B$ on the circle such that $\angle BOA=\frac{\pi}2-\psi$. Let $BB'$ be the altitude of the ...
• 85.7k

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