Question

Given the side lengths of 2, 2, and 3, the triangle is: 1:acute 2:obtuse 3:right 4:none are correct

Answer 1

2. obtuse

Explanation:

The side ratios of an isosceles right triangle are ...

1 : 1 : √2

Using a scale factor of 2, these would be ...

2 : 2 : 2√2 ≈ 2.828

Thus the long side of the given triangle is longer than necessary for a right triangle. That means, the opposite angle is larger than 90°.

The triangle is obtuse.

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You can find the exact value of the angles using the law of cosines. For the purpose of classifying the triangle, you need to know the angle opposite the longest side.

∠C = arccos((a²+b²-c²)/(2ab)) = arccos(((4+4-9)/(2·2·2)) = arccos(-1/8)

The cosine is negative only for angles greater than 90°, so the triangle is obtuse.