Question:
In a triangle \(ABC\), if \(a=2\), \(b=3\), and \(\sin A=\dfrac{2}{3}\), then \(\angle B=\)
In a triangle \(ABC\), if \(a=2\), \(b=3\), and \(\sin A=\dfrac{2}{3}\), then \(\angle B=\)
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When two sides and one opposite angle are given in a triangle, use the sine rule:
\[
\frac{a}{\sin A}=\frac{b}{\sin B}
\]
Updated On: Jun 26, 2026
- \(\dfrac{\pi}{2}\)
- \(\dfrac{\pi}{6}\)
- \(\dfrac{\pi}{3}\)
- \(\dfrac{\pi}{4}\)
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The Correct Option is A
Solution and Explanation
Step 1: Use sine rule.
In a triangle, \[ \frac{a}{\sin A}=\frac{b}{\sin B} \] Therefore, \[ \sin B=\frac{b\sin A}{a} \]
Step 2: Substitute the given values.
Given, \[ a=2,\quad b=3,\quad \sin A=\frac{2}{3} \] So, \[ \sin B=\frac{3\cdot \frac{2}{3}}{2} \]
Step 3: Simplify.
\[ \sin B=\frac{2}{2} \] \[ \sin B=1 \]
Step 4: Find angle \(B\).
Since, \[ \sin B=1 \] we get \[ B=\frac{\pi}{2} \]
Step 5: Final conclusion.
Therefore, \[ \boxed{\frac{\pi}{2}} \]
In a triangle, \[ \frac{a}{\sin A}=\frac{b}{\sin B} \] Therefore, \[ \sin B=\frac{b\sin A}{a} \]
Step 2: Substitute the given values.
Given, \[ a=2,\quad b=3,\quad \sin A=\frac{2}{3} \] So, \[ \sin B=\frac{3\cdot \frac{2}{3}}{2} \]
Step 3: Simplify.
\[ \sin B=\frac{2}{2} \] \[ \sin B=1 \]
Step 4: Find angle \(B\).
Since, \[ \sin B=1 \] we get \[ B=\frac{\pi}{2} \]
Step 5: Final conclusion.
Therefore, \[ \boxed{\frac{\pi}{2}} \]
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