Triangle ABC is obtuse when..
Triangle ABC is obtuse when one of its angles is greater than 90 degrees
Triangle ABC is obtuse when one of its angles is greater than 90 degrees. In other words, if any of the angles A, B, or C is greater than 90 degrees, the triangle is classified as obtuse.
To determine if a triangle is obtuse, you can use the properties of the triangle’s angles. The sum of the angles in any triangle is always 180 degrees. So, if all three angles in triangle ABC are less than 90 degrees, the sum of the angles would be less than 270 degrees, which is less than 180 degrees. Therefore, triangle ABC must have at least one angle greater than 90 degrees to make the total sum of angles 180 degrees.
For example, if angle A is 110 degrees, angle B is 35 degrees, and angle C is 35 degrees, the total sum of angles would be 110 + 35 + 35 = 180 degrees. In this case, angle A is greater than 90 degrees, making triangle ABC an obtuse triangle.
It is important to note that an obtuse triangle can only have one angle greater than 90 degrees. If two angles in a triangle are greater than 90 degrees, the sum of the angles will exceed 180 degrees, making it an invalid triangle according to Euclidean geometry.
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