Given triangle QRS with sides $q$ = $5$ units, $r$ = $6$ units, and the included angle $\angle \mathrm{QRS}$ = $60°$, what is the area of triangle QRS?

• A. $10$ square units
• B. $7$ square units
• C. $13$ square units
• D. $9$ square units

Answer: (A)

Verified step by step guidance

1. Identify the given elements in triangle QRS: side q = 5 units, side r = 6 units, and the included angle \( \angle QRS = 60^\circ \).
2. Recall the formula for the area of a triangle when two sides and the included angle are known: \[ \text{Area} = \frac{1}{2} \times q \times r \times \sin(\angle QRS) \].
3. Substitute the known values into the formula: \[ \text{Area} = \frac{1}{2} \times 5 \times 6 \times \sin(60^\circ) \].
4. Calculate \( \sin(60^\circ) \), which is a standard trigonometric value equal to \( \frac{\sqrt{3}}{2} \).
5. Multiply the values step-by-step: first multiply the sides and \( \frac{1}{2} \), then multiply by \( \sin(60^\circ) \) to find the area of triangle QRS.