\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}

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1. Let the diagonal be $$ d = 23.3 $$ inches and the angle between the diagonal and the bottom of the canvas be $$ \theta = 31^\circ $$.

2. The height, $$ h $$, which is opposite to the angle in the right triangle formed by the height, the width, and the diagonal, is given by
   $$
   h = d \cdot \sin(\theta)
   $$

3. Substituting the known values:
   $$
   h = 23.3 \cdot \sin(31^\circ)
   $$

4. Using a calculator, we approximate:
   $$
   \sin(31^\circ) \approx 0.5150
   $$
   so,
   $$
   h \approx 23.3 \cdot 0.5150 \approx 12.0 \text{ inches}
   $$

5. Rounding to the nearest inch, the height of the canvas is $$ 12 $$ inches.
The height of the canvas is 12 inches.

Louie is trying to find a rectangular canvas for his art project. Its diagonal must measure 23.3 inches and form a 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

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Louie is trying to find a rectangular canvas for his art project. Its diagonal must measure 23.3 inches and form a 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