Acute triangle

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An acute triangle is a triangle in which each angle is an acute angle. Any triangle which is not acute is either a right triangle or an obtuse triangle.

Acute triangles can also be defined in different ways:

  • A triangle is acute if and only if each of its altitudes lies entirely in the triangle's interior.
  • A triangle with sides of length $a, b$ and $c$ is acute if and only if $a^2 + b^2 > c^2$, $b^2 + c^2 > a^2$ and $c^2 + a^2 > b^2$. This is known as the Pythagorean Inequality.

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