Trigonometry & Inverse Trigonometry
Sine Rule in Triangles
Grade 11
Question:
<p>In △<i>ABC</i>, <i>a</i> = 4, <i>b</i> = 12 and <i>B</i> = 60°, then the value of sin <i>A</i> is</p>
<p>(a) \(\frac{1}{2\sqrt{3}}\)</p>
<p>(b) \(\frac{1}{3\sqrt{2}}\)</p>
<p>(c) \(\frac{1}{\sqrt{3}}\)</p>
<p>(d) \(\frac{1}{3}\)</p>
Step-by-Step Solution
Key Concept: Apply the sine rule to find the missing angle when two sides and one angle are known.
<p>Using the sine rule: $\frac{a}{\sin A} = \frac{b}{\sin B}$</p><p>$\frac{4}{\sin A} = \frac{12}{\sin 60°}$</p><p>$\sin A = \frac{4 \sin 60°}{12} = \frac{4 \cdot \frac{\sqrt{3}}{2}}{12} = \frac{1}{2\sqrt{3}}$</p>
Correct Answer: A