3. 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 light (ΔBDC)? Part 1: What other angles or sides of ΔBDC 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)

Part 2: Use the trigonometric ratios 30° and 60° to calculate and label the remaining sides of ΔBDC. 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 (ΔBDC)? Show your work. Use your calculator to round your final answer to the nearest foot. (3 points)

50 POINTS