AP EAMCET · Maths · Properties of Triangles
In a \(\triangle A B C\), if \(a=2, b=3\) and \(\sin A=\frac{2}{3}\), then \(\angle B=\)
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{6}\).
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(a=2, b=3, \sin A=\frac{2}{3}\) By sine rule, \(\frac{a}{\sin A}=\frac{b}{\sin B}\) \(\Rightarrow \quad \frac{2}{\frac{2}{3}}=\frac{3}{\sin B}\) \(\begin{aligned} \Rightarrow \quad \sin B & =1 \\ B & =\frac{\pi}{2}\end{aligned}\)
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