\begin{tabular}{l} Question 8 (Multiple Choice Worth 1 points) \\ (05.04 MC) \\ Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. If the rectangular frame's diagonal is 86.53 inches and forms a \( 56.31^{\circ} \) angle \\ with the bottom of the frame, what is its height? Round your answer to the nearest inch. \\ 48 inches \\ 56 inches \\ 72 inches \\ 131 inches \\ \hline\end{tabular}

To determine the height of the rectangular frame, Kendrick can use some trigonometry! Since he knows the diagonal length (86.53 inches) and the angle (56.31 degrees), he can apply the sine function. By using the formula: \[ \text{Height} = \text{Diagonal} \times \sin(\text{Angle}) \] Plugging in the values: \[ \text{Height} = 86.53 \times \sin(56.31^{\circ}) \] Calculating that gives him approximately 72 inches when rounded to the nearest inch. He should definitely measure again before purchasing but it seems like that beautiful painting will fit perfectly! In real-world application, understanding the dimensions of objects and angles can come in handy beyond just art. Whether you're rearranging furniture, hanging shelves, or planning home décor, using basic trigonometric principles helps ensure everything fits just right. So, next time you're measuring, remember: angles and diagonals can save you from a lot of headaches!