Understanding Obtuse Triangles: Definition, Classification, and Angle Measurement

obtuse triangle

An obtuse triangle is a type of triangle in which one of the angles is greater than 90 degrees

An obtuse triangle is a type of triangle in which one of the angles is greater than 90 degrees. This means that one of the angles inside the triangle is “obtuse” (greater than a right angle, which measures 90 degrees). The other two angles in an obtuse triangle are acute angles, meaning they are smaller than 90 degrees.

To determine if a triangle is obtuse, you need to examine the measures of its angles. If one of the angles is greater than 90 degrees, then the triangle is classified as an obtuse triangle.

Here’s an example: Let’s say we have a triangle with angles measuring 45 degrees, 60 degrees, and 75 degrees. To determine if this triangle is obtuse, we need to identify the largest angle. In this case, the largest angle is 75 degrees, which is greater than 90 degrees. Hence, this triangle is an obtuse triangle.

Obtuse triangles can have different types of classifications:

1. Acute-Obtuse Triangle: This is a triangle that has one acute angle and one obtuse angle.
2. Obtuse-Obtuse Triangle: This is a triangle that has two obtuse angles. The remaining angle in this case would be an acute angle.
3. Right-Obtuse Triangle: This is a triangle that has one right angle (90 degrees) and one obtuse angle. The remaining angle in this case would be an acute angle.

It is important to note that in any triangle, the sum of the interior angles always adds up to 180 degrees. Therefore, if you know the measures of two angles in a triangle, you can find the measure of the third angle by subtracting the sum of the known angles from 180 degrees.

In conclusion, an obtuse triangle is a triangle that has one angle greater than 90 degrees. By examining the measures of the angles, you can determine if a triangle is obtuse.

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