Carpeting a flight of stairs within budget

Core stretch

A flight of stairs has sloping length 8 m, width 2.5 m and slope angle \(30^\circ\). Carpet covers every horizontal tread and vertical riser. Carpet costs $22 per square metre and labour is $180. A budget of $850 is available. Determine whether it is sufficient. Give money amounts to 2 decimal places.[3]

Give non-exact lengths and areas to 3 significant figures, and angles to 1 decimal place.