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 the area of the triangle.</p>
<p>(a) 8</p>
<p>(b) 9</p>
<p>(c) 10</p>
<p>(d) 11</p>
Step-by-Step Solution
Key Concept: Apply the area formula $\text{Area} = \frac{1}{2}ab\sin C$ with the determined angle C.
Step 1: Determine the value of $\sin C$.
From the given information, it is determined that $\sin C = 1$.
Step 2: Calculate the area of the triangle.
The area of a triangle is given by the formula $\text{Area} = \frac{1}{2}ab\sin C$.
Substituting the given values $a=6$, $b=3$, and $\sin C = 1$:
$$ \text{Area} = \frac{1}{2} \times 6 \times 3 \times 1 = 9 $$
Correct Answer: B