Trigonometry & Inverse Trigonometry
Triangle Solution
Grade 11
Question:
<p>Given <i>a</i> = 6, <i>b</i> = 3 and \(\cos(A - B) = -\frac{1}{4}\), find \(\sin A\).</p>
<p>(a) \(\frac{\sqrt{5}}{2}\)</p>
<p>(b) \(\frac{4}{\sqrt{5}}\)</p>
<p>(c) \(\frac{\sqrt{5}}{3}\)</p>
<p>(d) \(\frac{3}{\sqrt{5}}\)</p>
Step-by-Step Solution
Key Concept: Use the sine rule combined with the law of cosines to find the remaining sides and angles.
<p><strong>Step 1:</strong> Using sine rule: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$</p><p><strong>Step 2:</strong> From the triangle with $C = \frac{3\pi}{4}$, we can find side <i>c</i> using cosine rule</p><p><strong>Step 3:</strong> Then apply sine rule to find $\sin A = \frac{a\sin C}{c}$, which gives $\sin A = \frac{4}{\sqrt{5}}$</p><p>∴ Answer is <i>B</i>.</p>
Correct Answer: B