Determining if a Triangle is Acute: Angle Measurements and Side Lengths Explained

acute triangle

An acute triangle is a triangle in which all three angles measure less than 90 degrees

An acute triangle is a triangle in which all three angles measure less than 90 degrees. In other words, an acute triangle has all angles that are acute (less than 90 degrees).

To determine if a triangle is acute, we can consider the measures of its angles. Here are two methods to determine if a triangle is acute:

1. Angle measurement method:
– Measure each angle of the triangle using a protractor.
– If all three angles measure less than 90 degrees, then the triangle is acute.
– If any angle measures 90 degrees or more, then the triangle is not acute.

2. Side length method (using the Pythagorean theorem):
– Consider the side lengths of the triangle.
– Label the sides of the triangle as a, b, and c, with c being the longest side.
– Apply the Pythagorean theorem: a^2 + b^2 = c^2.
– If a^2 + b^2 > c^2, then the triangle is acute.
– If a^2 + b^2 = c^2, then the triangle is right (a right triangle has one 90-degree angle).
– If a^2 + b^2 < c^2, then the triangle is obtuse (an obtuse triangle has one angle greater than 90 degrees). So, if all three angles of a triangle measure less than 90 degrees, it is an acute triangle.

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