\begin{tabular}{l} Louie is trying to find a rectangular canvas for his art project. Its diagonal must measure 23.3 inches and form a \( 31^{\circ} \) angle with the bottom of the canvas. What is the \\ height of the canvas? Round your answer to the nearest inch. \\ 12 inches \\ 14 inches \\ 24 inches \\ 27 inches \\ \\ \hline\end{tabular}

To find the height of the canvas, we can use some trigonometry. The diagonal of the rectangle acts as the hypotenuse of a right triangle, and the height corresponds to the opposite side. Using the sine function, we can express the height (h) as follows: \[ h = \text{diagonal} \times \sin(\theta) \] Here, the diagonal is 23.3 inches, and \(\theta\) is \(31^\circ\): \[ h = 23.3 \times \sin(31^\circ) \] Calculating this step-by-step: 1. Find \(\sin(31^\circ)\). This is approximately 0.515. 2. Now calculate \(h\): \[ h = 23.3 \times 0.515 \approx 12.0 \text{ inches} \] Rounding to the nearest inch gives us: \[ h \approx 12 \text{ inches} \] Thus, the height of the canvas is 12 inches.