Given side AB is 10 feet, and ∠ABC is trisected by BE and BD, we can determine the other angles and sides of triangle BDC. The angles are ∠DBC = 30° and ∠BDC = 90°, while the length of BD is 5√3 feet. Using trigonometric ratios, we find that BC = 5√3 feet and DC = 10 feet. By applying the Pythagorean Theorem, the length of BD is determined as 10√3 feet. Finally, the perimeter of triangle BDC is 35 feet.
Given that side AB is 10 feet and ∠ABC is trisected by BE and BD, we can use the properties of a triangle to find the other angles and sides of △BDC.
Using the properties of trisection, we can determine that ∠DBC is 30° and ∠BDC is 90°
We can also find that BD is 5√3 feet.
Therefore, the correct answer for Part 1 is a) ∠DBC = 30°, ∠BDC = 90°, BD = 5√3 feet.
In Part 2, using the trigonometric ratios for the angles 30° and 60°, we can calculate the remaining sides of △BDC.
We find that BC is 5√3 feet and DC is 10 feet.
Therefore, the correct answer for Part 2 is a) BC = 5√3 feet, DC = 10 feet.
In Part 3, we can use the Pythagorean Theorem to calculate the length of side BD.
Given that BC = 5√3 feet and DC = 10 feet, we can find that BD is 10√3 feet.
Therefore, the correct answer for Part 3 is c) BD = 10√3 feet.
In Part 4, to find the perimeter of the area to the right of the beam of light on Darcy's deck (△BDC), we need to add up the lengths of all three sides.
The lengths are BD = 10√3 feet, BC = 5√3 feet, and DC = 10 feet.
Adding these lengths, we get 10√3 + 5√3 + 10 = 15√3 + 10 feet.
Therefore, the correct answer for Part 4 is d) 35 feet.