In \(\triangle ABC\), if \(a = 2,\ b = 3,\ c = 4\), then prove that the triangle is obtuse angled.

Q.6 In \(\triangle ABC\), if \(a = 2,\ b = 3,\ c = 4\), then prove that the triangle is obtuse angled.

Doubtly Asked 28 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: \(\cos C = -\frac{1}{4} \lt 0\), so \(\angle C\) is obtuse.

The largest side is \(c = 4\), so the largest angle is \(C\). By the cosine rule,

\(\cos C = \frac{a^2 + b^2 - c^2}{2ab} = \frac{4 + 9 - 16}{2(2)(3)} = \frac{-3}{12} = -\frac{1}{4}\).

Since \(\cos C \lt 0\), \(\frac{\pi}{2} \lt C \lt \pi\), i.e. \(C\) is an obtuse angle. Hence the triangle is obtuse angled.

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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