Question

In triangle \( ABC \), 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. \( \frac{\pi}{4} \)

Hint:

Sine Rule Application}
Use \( \frac{a}{\sin A} = \frac{b}{\sin B} \) to solve for unknown angle
Solve algebraically and use arcsin for angle
If \( \sin B = 1 \Rightarrow B = 90^\circ \)

Answer 1

The Correct Option is A

Use sine rule: \[ \frac{a}{\sin A} = \frac{b}{\sin B} \Rightarrow \frac{2}{\frac{2}{3}} = \frac{3}{\sin B} \Rightarrow 3 = \frac{3}{\sin B} \Rightarrow \sin B = 1 \Rightarrow B = \frac{\pi}{2} \]