All acute triangle angles are less than 90 degrees. For example, an equilateral triangle is always acute, since all angles (which are 60) are all less than 90.
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 and is acute if and only if , and . This is known as the Pythagorean Inequality. It is a consequence of the Law of Cosines as the cosine of an angle that is less than 90 degrees is positive.
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