Given triangle QRS with sides $q$ and $r$ enclosing angle $S$, what is the formula for the area of triangle QRS?

• A. $\frac{1}{2}qrcosS$
• B. $\frac{1}{2}qrsinS$
• C. $\frac{1}{2}qrtanS$
• D. $qrsinS$

Answer: (B)

Verified step by step guidance

1. Recall that the area of a triangle can be found using the formula involving two sides and the included angle: \(\text{Area} = \frac{1}{2} \times \text{side}_1 \times \text{side}_2 \times \sin(\text{included angle})\).
2. Identify the two sides enclosing the angle \(S\) in triangle \(QRS\). These sides are given as \(q\) and \(r\).
3. Recognize that the included angle between sides \(q\) and \(r\) is angle \(S\).
4. Substitute the known sides and angle into the area formula: \(\text{Area} = \frac{1}{2} \times q \times r \times \sin(S)\).
5. Note that using \(\cos(S)\) or \(\tan(S)\) instead of \(\sin(S)\) in this formula would not correctly represent the area of the triangle.