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The side opposite to an obtuse angle of ...

The side opposite to an obtuse angle of a triangle is :

A

smallest

B

greatest

C

half of the perimeter

D

none of these

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The correct Answer is:
To solve the question about the side opposite to an obtuse angle in a triangle, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Triangle and the Obtuse Angle**: Let's denote the triangle as ABC. Assume angle A is the obtuse angle, meaning it is greater than 90 degrees. 2. **Understand the Properties of Angles and Sides**: In any triangle, the side opposite the largest angle is the longest side. Since angle A is obtuse, it is the largest angle in triangle ABC. 3. **Determine the Side Opposite the Obtuse Angle**: The side opposite angle A is side BC. Hence, BC is the side opposite the obtuse angle A. 4. **Compare the Lengths of the Sides**: According to the triangle inequality theorem, the side opposite the obtuse angle (BC) will be longer than the other two sides (AB and AC). Therefore, BC > AB and BC > AC. 5. **Conclusion**: Thus, the side opposite to the obtuse angle A in triangle ABC is the longest side, which is side BC. ### Final Answer: The side opposite to an obtuse angle of a triangle is the longest side of the triangle. ---
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