Please help with an act geo practice!! Please explain why I need help

Step-by-step explanation:

CD = 4sin30 = 4(1/2) = 2

∠BDC = 180 - 90 - 60 = 30°

BDcos30 = CD = 2

BD = 2/cos30 = 2/ (½√3) = 4/√3 = (4/3)√3

another way to do it would be

∠BDC = 180 - 90 - 60 = 30°

∠ADC = 180 - 90 - 30 = 60°

therefore

∠BDA = 60 - 30 = 30°

We can see the upper triangle is an isosceles triangle where lengths AB = BD and the angle between them is 180 - 30 - 30 = 120°

Using law of Sines

4/sin120 = BD/sin30

BD = 4sin30/sin120 = 4(½)/(½√3) = 4/√3 = (4/3)√3

or we could use the law of Cosines

c² = a² + b² - 2abcosC

BD² = AB² + 4² - 2(AB)(4)cos30

BD = AB = x

x² = x² + 4² - 2(x)(4)cos30

0 = 4² - 2(x)(4)cos30

4² = 2(x)(4)cos30

x = 4²/(2(4cos30)) = 2/cos30 = 2/ (½√3) = 4/√3 = (4/3)√3