Question

Help me out please need to figure this one out

Answer 1

Use the ratio of a 30-60-90 with the side opposite the 90 degree angle is 2x, the side opposite the 30 degree angle is x and the side opposite the 60 degree angle is x sqrt 3.If BC is 2 and angle CBD is 60 degrees, then angle DCB is 30 degrees. Therefore the side opposite the hypotenuse of BC is 1 (half of BC) and the side opposite the 60 degree angle is 1sqrt 3 or just sqrt 3.

Answer 2

Triangle BCD is 30 60 90 triangle
ratio of short leg: long leg : hypo = a : a√3 : 2a
Given hypo BC = 2 so short leg BD = 2/2 = 1
long leg CD = 1√3 = √3

Answer
CD = √3