AP EAMCET · Maths · Properties of Triangles
In \(\triangle \mathrm{ABC}\) if \(a=2 b\) and \(|\mathrm{A}-\mathrm{B}|=\frac{\pi}{3}\), then \(\angle \mathrm{C}=\)
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{2}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\(\frac{a}{\sin A} = \frac{b}{\sin B} \implies \frac{2b}{\sin A} = \frac{b}{\sin B} \implies \sin A = 2 \sin B\) Since \(\sin A = 2 \sin B\), then \(A > B\), so \(A - B = \frac{\pi}{3} \implies A = B + \frac{\pi}{3}\)…
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