\begin{tabular}{l} Jake is 6 ft . tall. He is standing outside \\ when the angle of elevation of the sun is \\ 28 degrees. How long would his shadow \\ be? \\ \( \qquad \)\begin{tabular}{c}11.3 feet \\ \hline 3.2 feet \\ \hline 28 feet \\ \hline 5.3 feet \end{tabular} \\ \hline \hline\end{tabular}

To solve this problem, we use some trigonometry! The height of Jake's head (6 ft) and the length of his shadow form a right triangle where the angle of elevation from the tip of the shadow to the top of his head is 28 degrees. Using the tangent function, which is the ratio of the opposite side (Jake's height) to the adjacent side (length of the shadow), we write: \[ \tan(28^\circ) = \frac{6 \text{ feet}}{\text{length of shadow}} \] Rearranging gives: \[ \text{length of shadow} = \frac{6 \text{ feet}}{\tan(28^\circ)} \] Using a calculator, we find that \(\tan(28^\circ) \approx 0.5317\). Therefore: \[ \text{length of shadow} \approx \frac{6}{0.5317} \approx 11.3 \text{ feet} \] So, the correct answer would be 11.3 feet! Did you know that shadows can actually help in determining the time of day? Ancient civilizations used sundials, which are essentially clocks that use the position of the sun to cast a shadow indicating the time! Additionally, understanding angles and shadows isn't just fun for outdoor activities—it has real-world applications in fields like architecture and solar energy. Designers optimize building orientations using this basic principle to reduce energy consumption or maximize light!