Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB = 10 feet, and BE and BD trisect ∠ABC, what is the perimeter of the deck area to the right of the beam of light (△BDC)? Part 1: What other angles or sides of △BDC can you label given that side AB is 10 feet, BE and BD trisect ∠ABC? Label the diagram accordingly, and explain your reasoning. (4 points) In a 30-60-90 right (special) angled triangle, the lengths are in the ratio 1:3–√:21:3:2. Part 2: Use the trigonometric ratios 30° and 60° to calculate and label the remaining sides of △BDC. Show your work. (3 points) Part 3: Use the Pythagorean Theorem to calculate the length of side BD. Does this method verify the length you found using trigonometric ratios? (2 points) Part 4: What is the perimeter of the area to the right of the beam of light on Darcy's deck (△BDC)? Show your work. Use your calculator to round your final answer to the nearest foot. (3 points)