# 8.10.5. Classification of Triangles According to Their Angles

Given that is an obtuse-angled triangle at , where cm and cm, then can equal cm.

• A42
• B27
• C35
• D54

### Example

Given that is an obtuse-angled triangle at , where cm and cm, then can equal cm.

• A42
• B27
• C35
• D54

### Solution

Since this triangle is obtuse-angled at , then the longest side is .

For every obtuse-angled triangle, the square length of the triangle's longest side is greater than the sum of the square lengths of the other two sides.

Write an inequality to show that the square length of is greater than the sum of the square lengths of the other two sides. Solve for the value of . (Approximate to the nearest hundredth.)

Of the possible lengths provided, and are the only lengths that are greater than . Therefore, , or .

The triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the other side. Therefore, it is not possible that because .

Therefore, .

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