Question

With usual notations in \( \triangle ABC \), \(a = 3\), \(c = 2\) and \(\sin C = \dfrac{2}{3}\), then \(\angle A =\)

• A. \( \dfrac{\pi}{4} \)
• B. \( \dfrac{\pi}{3} \)
• C. \( \dfrac{\pi}{2} \)
• D. \( \dfrac{\pi}{6} \)

Hint:

When \(\sin \theta = 1\), the angle must be \(90^\circ\) or \( \frac{\pi}{2} \) radians.

Answer 1

The Correct Option is C

Step 1: Apply the sine rule.
Using the sine rule in \( \triangle ABC \): \[ \frac{a}{\sin A} = \frac{c}{\sin C} \]
Step 2: Substitute the given values.
\[ \frac{3}{\sin A} = \frac{2}{2/3} \]
Step 3: Simplify the equation.
\[ \frac{2}{2/3} = 3 \Rightarrow \frac{3}{\sin A} = 3 \]
Step 4: Find angle \(A\).
\[ \sin A = 1 \Rightarrow A = \frac{\pi}{2} \]