4 Multiple Answer 1 point Ben made a sundial in his backyard by placing a stick with height 6 io sth ground making a 90 degree angle with the ground, and marking the hou grass. To test it, he checks the time each day when the sun makes an ane \( 60^{\circ} \) with the ground. Select all the possible lengths of the shadow whe the sundial. The shadow will be the side of the triangle opposite the 30 on angle. 12 in \( 2 \sqrt{2} \) in \( 6 \sqrt{3} \) in 8 in \( 2 \sqrt{3} \) in

To find the length of the shadow when the sun makes a \( 60^{\circ} \) angle with the ground, we can use trigonometry. The height of the stick (6 inches) represents the opposite side of the triangle, while the shadow will be the adjacent side. Using the tangent function: \[ \tan(60^{\circ}) = \frac{6}{\text{shadow length}} \] Since \(\tan(60^{\circ}) = \sqrt{3}\), we have: \[ \sqrt{3} = \frac{6}{\text{shadow length}} \Rightarrow \text{shadow length} = \frac{6}{\sqrt{3}} = 2\sqrt{3} \text{ in} \] Now, let's calculate the other options: - For \(12 \text{ in}\): Not possible, as the shadow can't exceed the height at this angle. - For \(2\sqrt{2} \text{ in}\): Also incorrect because it doesn't match our calculation. - For \(6\sqrt{3} \text{ in}\): Too long for this configuration based on the angle. - For \(8 \text{ in}\): Incorrect as well due to the height limiting the shadow length. Thus, the **only possible option** is \(2 \sqrt{3} \text{ in}\). The confirmed answer is \(2 \sqrt{3} \text{ in}\).