Q.1 (ii) In triangle ABC , if a = 2,\ b = 3 and sin A = 2/3 , then ∠ B = _____ A. π/2 B. π/3 C. π/4 D. π/6

Answer: A. π/2 Answer: (a) π/2 By the sine rule, a/sin A = b/sin B , so sin B = b sin A/a = 3 · 2/3/2 = 1 . Hence B = π/2 .

In \(\triangle ABC\), if \(a = 2,\ b = 3\) and \(\sin A = \frac{2}{3}\), then \(\angle B =\) _____

Q.1 (ii) In \(\triangle ABC\), if \(a = 2,\ b = 3\) and \(\sin A = \frac{2}{3}\), then \(\angle B =\) _____

A. \(\frac{\pi}{2}\)

B. \(\frac{\pi}{3}\)

C. \(\frac{\pi}{4}\)

D. \(\frac{\pi}{6}\)

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

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Answer: A. \(\frac{\pi}{2}\)

Answer: (a) \(\frac{\pi}{2}\)

By the sine rule, \(\frac{a}{\sin A} = \frac{b}{\sin B}\), so \(\sin B = \frac{b \sin A}{a} = \frac{3 \cdot \frac{2}{3}}{2} = 1\). Hence \(B = \frac{\pi}{2}\).

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

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In \(\triangle ABC\), if \(a = 2,\ b = 3\) and \(\sin A = \frac{2}{3}\), then \(\angle B =\) _____

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