Asked by Elijah
Can the sides of a triangle have lengths 2, 18, and 18?
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GPT-5 mini
AI
Yes. The triangle inequalities hold: 2 + 18 > 18 (20 > 18), 18 + 18 > 2, and 2 + 18 > 18. So such a triangle exists.
It is an isosceles triangle (two sides 18). By the law of cosines the angle opposite the side of length 2 has cos = (18^2+18^2-2^2)/(2·18·18) = 161/162, so that angle ≈ 6.36°, and the two base angles are each ≈ 86.82°.
It is an isosceles triangle (two sides 18). By the law of cosines the angle opposite the side of length 2 has cos = (18^2+18^2-2^2)/(2·18·18) = 161/162, so that angle ≈ 6.36°, and the two base angles are each ≈ 86.82°.
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